Question

Consider the trinomial x2 – 9x + 18. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?

Answer 1

x^2 - 9x + 18
AC = 18
Factors of AC: 1 * 18, 2 * 9, 3 * 6, -1 * -18, -2 * -9, -3 * -6
Sum to -9: 19, 11, 9, -19, -11, -9

(x - 3)(x - 6)

Answer 2

The required pair of number are -3 and -6

The factored form of the trinomial is (x-3) and (x-6)

The standard form of a quadratic equation is expressed as:

$ax^2+bx+c=0$

Given the expression $x^2 - 9x + 18.$

$a=1\\b=-9\\c=18$

We are to get two values that we must add to get b, and that we will multiply that will give c.

The given values are -6 and -3

Check:

$-6+(-3)=-6-3=-9\\-6(-3) = 18$

Factorize the trinomial

$x^2-9x+18\\x^2-6x-3x+18\\x(x-6)-3(x-6)\\(x-3)(x-6)$

Hence the factored form of the trinomial is (x-3) and (x-6).

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