Question

factor completely.
$5x^{2}+6x - 8$
answer
attempt 1 out of 2

Explanation:

Step1: Multiply coefficients

Multiply the coefficient of $x^{2}$ (5) and the constant term (-8), we get $5\times(-8)= - 40$.

Step2: Find two - numbers

Find two numbers that multiply to - 40 and add up to the coefficient of $x$ (6). The numbers are 10 and - 4 since $10\times(-4)=-40$ and $10+( - 4)=6$.

Step3: Rewrite the middle term

Rewrite the middle term $6x$ as $10x-4x$. So, $5x^{2}+6x - 8=5x^{2}+10x-4x - 8$.

Step4: Group the terms

Group the terms: $(5x^{2}+10x)+(-4x - 8)$.

Step5: Factor out the GCF from each group

Factor out the greatest common factor (GCF) from each group. From the first group $5x^{2}+10x$, the GCF is $5x$, so $5x^{2}+10x = 5x(x + 2)$. From the second group $-4x - 8$, the GCF is - 4, so $-4x - 8=-4(x + 2)$.

Step6: Factor out the common binomial factor

We have $5x(x + 2)-4(x + 2)$. Factor out the common binomial factor $(x + 2)$ to get $(x + 2)(5x-4)$.

Answer:

$(x + 2)(5x-4)$