Question

Factors of 18x² + 6x-4?

Answer 1

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

Explanation:

18x² + 6x - 4 ← factor out 2 from each term

= 2(9x² + 3x - 2) ← factor the quadratic

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 - 3 and + 6

use these factors to split the x- term

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

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

= (3x - 1)(3x + 2) ← in factored form

then

18x² + 6x - 4

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

Answer 2

`\huge\boxed{\bf\:2\left(3x-1\right)\left(3x+2\right) }`

Explanation:

`18x^(2) + 6x - 4\\\\Factor \: out \: the \: common \: factor = 2\\\\= 2\left(9x^(2)+3x-2\right) \\\\Split\:the\:quadraric\:equation\:inside\:the\:parentheses \\\:using\:the\:splitting-the-middle-term \:method.\\\\= 2\left(9x^(2)-3x\right)+\left(6x-2\right) \\= 2 (3x\left(3x-1\right)+2\left(3x-1\right) )\\= \boxed{\bf\:2 \left(3x-1\right)\left(3x+2\right) }`

`\rule{150pt}{2pt}`