Question

select the correct answer.
factor the following expression.
15x^{2}+5x - 50
5(x + 2)(3x - 5)
5(x + 5)(3x - 2)
5(x - 2)(3x + 5)
5(x - 5)(3x + 2)

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor (GCF) of the coefficients 15, 5, and 50. The GCF of 15, 5, and 50 is 5. So, we can rewrite the expression as $5(3x^{2}+x - 10)$.

Step2: Factor the quadratic expression

We need to factor the quadratic expression $3x^{2}+x - 10$. We use the AC - method. For the quadratic $ax^{2}+bx + c$ (here $a = 3$, $b = 1$, $c=-10$), we find $ac=3\times(-10)=-30$. We need to find two numbers that multiply to - 30 and add up to 1. The numbers are 6 and - 5 since $6\times(-5)=-30$ and $6+( - 5)=1$.
Rewrite the middle term: $3x^{2}+6x-5x - 10$.
Group the terms: $(3x^{2}+6x)-(5x + 10)$.
Factor out the common factors from each group: $3x(x + 2)-5(x + 2)$.
Then, factor out $(x + 2)$: $(x + 2)(3x-5)$.
So, $15x^{2}+5x - 50=5(x + 2)(3x - 5)$.

Answer:

$5[(x + 2)(3x - 5)]$