Question

factor completely.

$2x^{2}+5x + 2$

answer

attempt 1 out of 2

Explanation:

Step1: Multiply coefficients

Multiply the coefficient of $x^{2}$ (which is 2) and the constant term (which is 2). So, $2\times2 = 4$.

Step2: Find two - numbers

Find two numbers that multiply to 4 and add up to 5. The numbers are 4 and 1 since $4\times1=4$ and $4 + 1=5$.

Step3: Rewrite the middle term

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

Step4: Group the terms

Group the terms: $(2x^{2}+4x)+(x + 2)$.

Step5: Factor out the GCF from each group

Factor out the greatest - common factor (GCF) from each group. From $2x^{2}+4x$, the GCF is $2x$, so $2x^{2}+4x=2x(x + 2)$. From $x + 2$, the GCF is 1. Then we have $2x(x + 2)+1(x + 2)$.

Step6: Factor out the common binomial factor

Factor out the common binomial factor $(x + 2)$. So, $2x(x + 2)+1(x + 2)=(2x + 1)(x + 2)$.

Answer:

$(2x + 1)(x + 2)$