Question

consider the trinomial $x^2 - 9x + 18$. which pair of numbers has a product of $ac$ and a sum of $b$? what is the factored form of the trinomial?

Explanation:

Step1: Identify a, b, c values

For $x^2 - 9x + 18$, $a=1$, $b=-9$, $c=18$

Step2: Calculate $ac$ product

$ac = 1 \times 18 = 18$

Step3: Find pair with product 18, sum -9

The pair $-3$ and $-6$: $(-3) \times (-6)=18$, $(-3)+(-6)=-9$

Step4: Factor the trinomial

Split middle term: $x^2 -3x -6x +18$, group and factor:
$x(x-3)-6(x-3)=(x-3)(x-6)$

Answer:

1. The pair of numbers: $-3$ and $-6$
2. The factored form: $(x-3)(x-6)$