Trinomials - PSAT Math

Find the product:

Step 1: Use the Distributive Property

Step 2: Combine like terms

Find the product:

Use the distributive property:

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:

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:

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 .

Find the quotient:

Step one: Factor the numerator

Step two: Simplify

Find the quotient:

Step one: Factor the numerator

Step two: Simplify

With this problem, you need to take the trinomials out of parentheses and combine like terms. Since the two trinomials are being added together, you can remove the parentheses without needing to change any signs:

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:

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: