Identify the value of b. Considering k>0, find pair of numbers with a sum of b.
7, 12, 15, 16
Practice makes perfect
We want to find the possible k-values so that the given expression can be factored using integers.
x^2-8x+k, k>0
⇕
x^2+( - 8)x+k, k>0
In this trinomial, b= - 8. Since k>0 and b is negative, we need to find two factors with the same sign and a sum of - 8. Therefore, both factors should be negative. Let's list pairs of numbers whose sum is - 8 and find their product.
c|c
Pair of & Product of
numbers & numbers [0.4em] [-0.6em]
- 1, - 7 & 7
- 2, - 6 & 12
- 3, - 5 & 15
- 4, - 4 & 16
When k is 7, 12, 15, or 16, the expression can be factored.
