Identify the value of b. Considering k>0, find pair of numbers with a sum of b.
4, 6
Practice makes perfect
We want to find the possible k-values so that the given expression can be factored using integers.
x^2-5x+k, k>0
⇕
x^2+( - 5)x+k, k>0
In this trinomial, b= - 5. 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 - 5 and find their product.
c|c
Pair of numbers & Product of
with a sum of - 5 & numbers [0.4em] [-0.6em]
- 1, - 4 & 4
- 2, - 3 & 6
When k is either 4 or 6, the expression can be factored.
