Problems 63-112 should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. (Objective 4)
The given expression .
To factor trinomials of the form , we first assume .
Step-2: Rewrite the trinomial as .
Let us consider a product .
Using the distributive property of multiplication, we get
From the above, we find that the product of yields a trinomial of the form .
It must be noted that the middle term is the sum of and and the last term is the product of and .
These two relationships can be used for factoring trinomials of the form .
Step-3: Substitute back to get the solution.
Rewrite the given trinomial as
We need to complete the following with two integers whose sum is and whose product is .
The following table shows the possible pairs of factors of and the sum of integers:
|Factors||Product of the factors||Sum of the factors|
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