Question

question
factor the trinomial:
5x^2 + 11x + 2

Explanation:

Step1: Multiply leading - coefficient and constant

Multiply 5 (leading coefficient) and 2 (constant). $5\times2 = 10$.

Step2: Find two numbers for 10

Find two numbers that multiply to 10 and add up to 11. The numbers are 10 and 1 since $10\times1=10$ and $10 + 1=11$.

Step3: Rewrite the middle term

Rewrite $11x$ as $10x+x$. So, $5x^{2}+11x + 2=5x^{2}+10x+x + 2$.

Step4: Group the terms

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

Step5: Factor out the GCF from each group

Factor out the greatest - common factor (GCF) from each group. From $5x^{2}+10x$, the GCF is $5x$, so $5x^{2}+10x = 5x(x + 2)$. From $x + 2$, the GCF is 1. So, $(5x^{2}+10x)+(x + 2)=5x(x + 2)+1(x + 2)$.

Step6: Factor out the common binomial

Factor out the common binomial $(x + 2)$. We get $(5x + 1)(x+2)$.

Answer:

$(5x + 1)(x + 2)$