Trinomials - ACT Math
Card 0 of 20
Choose the answer which best simplifies the following expression:
Choose the answer which best simplifies the following expression:
To solve this problem simply remove the parentheses and add the like terms:
To solve this problem simply remove the parentheses and add the like terms:
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Add 
and 
.
Add
To add the trinomials, simply eliminate the parentheses and add like terms.
To add the trinomials, simply eliminate the parentheses and add like terms.
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Like terms can be added together: 
is added to 
, 
is added to 
, and 
is added to 
. The resulting answer choice that is correct is 
.
Like terms can be added together:
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Choose the answer which best simplifies the following expression:
Choose the answer which best simplifies the following expression:
To simplify, simply remove the parentheses and combine like terms:
To simplify, simply remove the parentheses and combine like terms:
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Choose the answer which best simplifies the following expression:
Choose the answer which best simplifies the following expression:
To simplify, remove parentheses and combine like terms:
To simplify, remove parentheses and combine like terms:
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Choose the answer which best simplifies the following expression:
Choose the answer which best simplifies the following expression:
To simplify, remove parentheses and combine like terms:
Note that adding or subtracting a zero to the end of this equation is unnecessary.
To simplify, remove parentheses and combine like terms:
Note that adding or subtracting a zero to the end of this equation is unnecessary.
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Divide:
Divide:
can be divided using long division.
The set up would look very similar to the division of real numbers, such as when we want to divide 10 by 2 and the answer is 5.
The first step after setting up the "division house" is to see what the first term in the outer trinomial needs to multiplied by to match the 
in the house. In this case, it's 
. 
will be multiplied across the other two terms in the outer trinomial and the product will be subtracted from the expression inside the division house. The following steps will take place in the same way.
While we could continue to divide, it would require the use of fraction exponents that would make the answer more complicated. Therefore, the term in red will be the remainder. Because this remainder is still subject to be being divided by the trinomial outside of the division house, we will make the remainder part of the final answer by writing it in fraction form:
Therefore the final answer is
The set up would look very similar to the division of real numbers, such as when we want to divide 10 by 2 and the answer is 5.
The first step after setting up the "division house" is to see what the first term in the outer trinomial needs to multiplied by to match the
While we could continue to divide, it would require the use of fraction exponents that would make the answer more complicated. Therefore, the term in red will be the remainder. Because this remainder is still subject to be being divided by the trinomial outside of the division house, we will make the remainder part of the final answer by writing it in fraction form:
Therefore the final answer is
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Simplify the expression:
Simplify the expression:
Once simplified, (x+1) appears on both the numerator and denominator, meaning we can cancel out both of them.
Which gives us:
Once simplified, (x+1) appears on both the numerator and denominator, meaning we can cancel out both of them.
Which gives us:
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Find the 
-intercepts:
Find the
-intercepts occur when 
.
1. Set the expression equal to 
and rearrange:
2. Factor the expression:
3. Solve for 
:
and...
4. Rewrite the answers as coordinates:
becomes 
and 
becomes 
.
1. Set the expression equal to
2. Factor the expression:
3. Solve for
and...
4. Rewrite the answers as coordinates:
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Solve for 
when 
.
Solve for
1. Factor the expression:
2. Solve for 
:
and...
1. Factor the expression:
2. Solve for
and...
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Factor the following expression:
Factor the following expression:
Remember that when you factor a trinomial in the form 
, you need to find factors of 
that add up to 
.
First, write down all the possible factors of 
.
Then add them to see which one gives you the value of 
Thus, the factored form of the expression is 
Remember that when you factor a trinomial in the form
First, write down all the possible factors of
Then add them to see which one gives you the value of
Thus, the factored form of the expression is
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Factor the expression completely
Factor the expression completely
First, find any common factors. In this case, there is a common factor: 
Now, factor the trinomial.
To factor the trinomial, you will need to find factors of 
that add up to 
.
List out the factors of 
, then add them.
Thus, 
First, find any common factors. In this case, there is a common factor:
Now, factor the trinomial.
To factor the trinomial, you will need to find factors of
List out the factors of
Thus,
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Which expression is equivalent to the polynomial 
.
Which expression is equivalent to the polynomial
This question calls for us to factor the polynomial into two binomials. Since the first term is 
and the last term is a number without a variable, we know that how answer will be of the form 
where a and b are positive or negative numbers.
To find a and b we look at the second and third term. Since the second term is 
we know 
. (The x comes from a and b multiplying by x and then adding with each other). The +10 term tells us that 
. Using these two pieces of information we can look at possible values. The third term tells us that 1 & -10 and -1 & 10 are the possible pairs. Now we can look and see which one adds up to make 9. This gives us the pair -1 & 10 and we plug that into the equation as a and b to get our final answer.
This question calls for us to factor the polynomial into two binomials. Since the first term is
To find a and b we look at the second and third term. Since the second term is
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Which expression is equivalent to the following polynomial: 
Which expression is equivalent to the following polynomial:
This question calls for us to factor the polynomial into two binomials. Since the first term is 
and the last term is a number without a variable, we know that how answer will be of the form 
where a and b are positive or negative numbers.
To find a and b we look at the second and third term. Since the second term is 
we know 
. (The x comes from a and b multiplying by x and then adding with each other). The -14 term tells us that 
. Using these two pieces of information we can look at possible values. The third term tells us that 1 & -14, 2 & -7, -2 & 7, and -1 & 14 are the possible pairs. Now we can look and see which one adds up to make 5. This gives us the pair -2 & 7 and we plug that into the equation as a and b to get our final answer.
This question calls for us to factor the polynomial into two binomials. Since the first term is
To find a and b we look at the second and third term. Since the second term is
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Which expression is equivalent to the following polynomial:
Which expression is equivalent to the following polynomial:
This question calls for us to factor the polynomial into two binomials. Since the first term is 
and the last term is a number without a variable, we know that how answer will be of the form 
where a and b are positive or negative numbers.
To find a and b we look at the second and third term. Since the second term is 
we know 
. (The x comes from a and b multiplying by x and then adding with each other). The 
term tells us that 
. Using these two pieces of information we can look at possible values. The third term tells us that 1 & 8, 2 & 4, -2 & -4, and -1 & -8 are the possible pairs. Now we can look and see which one adds up to make -9. This gives us the pair -1 & -8 and we plug that into the equation as a and b to get our final answer.
This question calls for us to factor the polynomial into two binomials. Since the first term is
To find a and b we look at the second and third term. Since the second term is
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Simplify the following:
Simplify the following:
To multiply trinomials, simply foil out your factored terms by multiplying each term in one trinomial to each term in the other trinomial. I will show this below by spliting up the first trinomial into its 3 separate terms and multiplying each by the second trinomial.
Now we treat this as the addition of three monomials multiplied by a trinomial.
Now combine like terms and order by degree, largest to smallest.
To multiply trinomials, simply foil out your factored terms by multiplying each term in one trinomial to each term in the other trinomial. I will show this below by spliting up the first trinomial into its 3 separate terms and multiplying each by the second trinomial.
Now we treat this as the addition of three monomials multiplied by a trinomial.
Now combine like terms and order by degree, largest to smallest.
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Solve: 
Solve:
The 
is distributed and multiplied to each term 
, 
, and 
.
The
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Which of the following is equal to 
?
Which of the following is equal to
is multiplied to both 
and 
and 
is only multiplied to 
.
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What is 
?
What is
is distributed first to 
and 
is distributed to 
. This results in 
and 
. Like terms can then be added together. When added together, 
, 
, and 
. This makes the correct answer 
.
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A hockey team has 12 forwards, 6 defensemen, and 2 goalies. When they place 3 forwards, 2 defensemen, and 1 goalie on the ice, how many of each type are on the bench, (not on the ice)? F=Forward, D = Defensemen, G= Goalie
A hockey team has 12 forwards, 6 defensemen, and 2 goalies. When they place 3 forwards, 2 defensemen, and 1 goalie on the ice, how many of each type are on the bench, (not on the ice)? F=Forward, D = Defensemen, G= Goalie
We can represent this as a subtraction of trinomials.
(12F + 6D + 2G) – (3F + 2D + 1G) = 9F + 4D + 1G.
We can represent this as a subtraction of trinomials.
(12F + 6D + 2G) – (3F + 2D + 1G) = 9F + 4D + 1G.
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