Question

Solve the following equation by factoring: 9x^2 – 3x – 2 = 0

Answer choices:
A.x=-1/3 or x=2/3
B.x=-2/3 or x=1/3
C.x=-2/3 or x=-1/3
D.x=1/3 or x=2/3

Answer 1

A

Explanation:

Given

9x² - 3x - 2 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 9 × - 2 = - 18 and sum = - 3

The factors are - 6 and + 3

Use these factors to split the x- term

9x² - 6x + 3x - 2 = 0 ( factor the first/second and third/fourth terms )

3x(3x - 2) + 1(3x - 2) ← factor out (3x - 2) from each term

(3x - 2)(3x + 1) = 0

Equate each factor to zero and solve for x

3x - 2 = 0 ⇒ 3x = 2 ⇒ x =
`(2)/(3)`

3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = -
`(1)/(3)`

Answer 2

The answer is A. X=-1/3 or x=2/3