Arithmetic with Polynomials & Rational Expressions - Common Core: High School - Algebra

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the term down.

Now we multiply the zero by the term we just put down, and place it under the term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at -2 and 3, thus verifying the results found by factorization.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at 3 and 4, thus verifying the results found by factorization.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at -3 and -6, thus verifying the results found by factorization.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at -4 and 2, thus verifying the results found by factorization.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at -1, thus verifying the result found by factorization.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at -6 and -1, thus verifying the results found by factorization.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at -1 and -3, thus verifying the results found by factorization.

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a value equal to zero.

One technique that can be used is factorization. In general form,

where,

and are factors of and when added together results in .

For the given function,

the coefficients are,

therefore the factors of that have a sum of are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

The graph crosses the -axis at 1, thus verifying the result found by factorization.