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 trinomial.
8x^2+10x-21
First, notice that there is no greatest common factor.
There are two additional common factoring techniques for trinomials.
Since 21 is not a perfect square, 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.
8x^2+10x-21 ⇔ 8x^2+ 10x +( -21)
For our expression, we have that a= 8, b= 10, and c= - 21. 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 product is 8( -21)=-168 and the sum is 10. Let's do it!
Factor Pair
Product
Sum
-1 and 168
-1* 168 - 168
-1+168 167
- 2 and 84
- 2* 84 -168
- 2+84 82
-3 and 56
-3* 5 -168
-3+56 53
- 4 and 42
- 4* 42 -168
- 4+42 38
-6 and 28
-6* 28 - 168
-6+28 22
- 7 and 24
- 7* 24 - 168
- 7+24 17
-8 and 21
-8* 21 - 168
-8+21 13
- 12 and 14
- 12* 14 - 168
- 12+14 2
We cannot find a pair of integers whose product is -168 and whose sum is 10. Therefore, we cannot use the general method for factoring trinomials. The given polynomial cannot be factored, so it is prime.
