How do you factor 9x ^ { 2} + 21x - 189x2+21x18?

2 Answers
Jul 21, 2017

To factor 9x2+21x−189x2+21x18

Factor out the 33: 3(3x^2+7x-6)3(3x2+7x6)
Continue factoring: 3(3x-2)(x+3)3(3x2)(x+3)

Sep 10, 2017

3(3x - 2)(x + 3)3(3x2)(x+3)

Explanation:

f(x) = 9x^2 + 21x - 18 = 3(3x^2 + 7x - 6)f(x)=9x2+21x18=3(3x2+7x6)

Factor the trinomial in parentheses by the new AC Method (Socratic, Google Search)

y = 3x^2 + 7x - 6 = 3(x + p)(x + q)y=3x2+7x6=3(x+p)(x+q)

Factor converted trinomial:
y' = x^2 + 7x - 18 = (x + p')(x + q').

Find p' and q'

knowing the sum (b = 7) and the product (ac = - 18).

They are: p' = -2 and q' = 9 rarr ["sum " = 7 and " product " = - 18]

Back to y:

p = (p')/a = -2/3 , and q = (q')/a = 9/3 = 3

Factored form of f(x):

f(x) = 3(3)(x - 2/3)(x + 3) = 3(3x - 2)(x + 3)