Trinomials - PSAT Math

With this problem, you need to distribute the two fractions across each of the trinomials. To do this, you multiply each term inside the parentheses by the fraction outside of it:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms. Since you have a positive and negative , those two terms will cancel out:

To add these two trinomials, you will first begin by combining like terms. You have two terms with , two terms with , and two terms with no variable. For the two fractions with , you can immediately add because they have common denominators:

To add trinomials, identify and group together the like-terms: . Next, factor out what is common between the like-terms:. Finally, add what is left inside the parentheses to obtain the final answer of .

All operations are addition, so we can first remove the parentheses:

Now rearrange the terms so that like terms are next to each other:

Combine like terms:

Find the sum:

Write the answer in standard form.

Combine like terms:

Write the answer in standard form (terms with the highest degree first):

Find the quotient:

Step one: Factor the numerator

Step two: Simplify

We must begin by factoring out from each term.

Next, we must find two numbers that sum to and multiply to .

Thus, our final answer is:

To trinomial is in form

In order to factor, find two numbers whose procuct is , in this case , and whose sum is , in this case

Factors of :

Which of these pairs has a sum of ?

and

Therefore the factored form of is:

Our factors will need to have a product of , and a sum of , so our factors must be and .

Use the distributive property:

Combine like terms:

Find the product:

Step 1: Use the Distributive Property

Step 2: Combine like terms

Find the product:

Use the distributive property:

To subtract these two trinomials, you first need to flip the sign on every term in the second trinomial, since it is being subtrated:

Next you can combine like terms. You have two terms with , two terms with , and two terms with no variable:

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses:

Next, identify and group the like terms in order to combine them: .

Find the difference:

Distribute the negative to the second trinomial:

Combine like terms: