question\nfactor completely.\n$2x^{2}+15x + 25$

Answer

Explanation:

Step1: Multiply leading - coefficient and constant

Multiply 2 (leading coefficient) and 25 (constant), $2\times25 = 50$.

Step2: Find two numbers

Find two numbers that multiply to 50 and add up to 15. The numbers are 10 and 5 since $10\times5=50$ and $10 + 5=15$.

Step3: Rewrite the middle term

Rewrite $15x$ as $10x+5x$. So, $2x^{2}+15x + 25=2x^{2}+10x+5x + 25$.

Step4: Group the terms

Group the terms: $(2x^{2}+10x)+(5x + 25)$.

Step5: Factor out the GCF from each group

Factor out the greatest - common factor (GCF) from each group. From $2x^{2}+10x$, the GCF is $2x$, so $2x^{2}+10x=2x(x + 5)$. From $5x + 25$, the GCF is 5, so $5x + 25=5(x + 5)$.

Step6: Factor out the common binomial factor

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

Answer:

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