Is there a greatest common factor? What other factoring technique could be used according to the number of terms?
Prime
Practice makes perfect
We want to factor the given polynomial. Note that it has three terms.
4x^2+9x-16
First, note that there is no greatest common factor.
There are two additional common factoring techniques for trinomials.
Note that 16 and 4x^2 are perfect squares. However, 9x≠2* 4* 2x, so the given expression is not a perfect square trinomial. Let's try the other method. First, we will identify the values a, b, and c.
4x^2+9x-16 ⇔ 4x^2+ 9x +( -16)
For our expression, we have that a= 4, b= 9, and c= - 16. We want to check if we can find a pair of integers with a product of a * c and a sum of b. In this case, the desired product is 4( -16)=-64 and the sum we are looking for is 9. Let's do it!
Factor Pair
Product
Sum
-1 and 64
-1* 64 - 64
-1+64 63
- 2 and 32
- 2* 32 -64
- 2+32 30
-4 and 16
-4* 16 -64
-4+16 12
-8 and 8
-8* 8 - 64
-8+8 0
We cannot find a pair of integers whose product is -64 and whose sum is 9. Therefore, we cannot use the general method for factoring trinomials. The given polynomial cannot be factored, so it is prime.
