Question

home > math 141 (precalculus i) fall 2025 ls online > assessment intermediate algebra diagnostic score: 10/20 answered: 11/20 question 12 factor $2x^{2}+11x + 5$ question help: video submit question

Explanation:

Step1: Multiply coefficients

Multiply the coefficient of $x^{2}$ (which is 2) and the constant term 5. So, $2\times5 = 10$.

Step2: Find two - numbers

Find two numbers that multiply to 10 and add up to 11. The numbers are 1 and 10 since $1\times10=10$ and $1 + 10=11$.

Step3: Rewrite the middle term

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

Step4: Group the terms

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

Step5: Factor out the GCF from each group

From the first group $2x^{2}+x$, the GCF is $x$, so $2x^{2}+x=x(2x + 1)$. From the second group $10x + 5$, the GCF is 5, so $10x + 5=5(2x+1)$.

Step6: Factor out the common binomial factor

We have $x(2x + 1)+5(2x + 1)=(2x + 1)(x + 5)$.

Answer:

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