Question

which is a factor of $30x^2 - 4x - 16$?
$5x - 4$
$3x - 4$
$3x - 2$
$5x + 4$
clear all

Explanation:

Step1: Factor the quadratic expression

We can factor $30x^2 - 4x - 16$ by first factoring out a common factor of 2:
$30x^2 - 4x - 16 = 2(15x^2 - 2x - 8)$
Now factor $15x^2 - 2x - 8$ by finding two numbers that multiply to $15\times(-8)=-120$ and add to $-2$. These numbers are $-12$ and $10$.
Rewrite the middle term:
$15x^2 -12x +10x -8 = 3x(5x - 4) + 2(5x - 4) = (3x + 2)(5x - 4)$
So the full factorization is:
$30x^2 - 4x - 16 = 2(3x + 2)(5x - 4)$

Step2: Match with options

Compare the factors to the given choices.

Answer:

A. $5x - 4$