Question

Which is a factor of 18x2 + 3x − 6?
2x+1
2x+3
3x+2
3x-1

Answer 1

`18x^2+3x-6=18x^2+12x-9x-6=6x(3x+2)-3(3x+2)\\=(3x+2)(6x-3)=3(3x+2)(2x-1)`

Answer 2

The correct option is C. (3·x + 2)

Explanation:

The quadratic equation is given to be : 18·x² + 3·x - 6

We need to find the factors of this given quadratic equation.

Let f(x) = 18·x² + 3·x - 6

⇒ f(x) = 3 × (6·x² + x - 2)

⇒ f(x) = 3 × (6·x² - 3·x + 4·x - 2)

⇒ f(x) = 3 × [3·x(2·x - 1) + 2(2·x - 1)]

⇒ f(x) = 3·(2·x - 1)·(3·x + 2)

Now, from the given options : The required factor of the given quadratic equation is (3·x + 2)

Therefore, The correct option is C. (3·x + 2)