factor.\n$5x^{2}+27x + 10$

Answer

Explanation:

Step1: Multiply coefficients

Multiply the coefficient of $x^{2}$ (which is 5) and the constant term (which is 10). So, $5\times10 = 50$.

Step2: Find factor - pair

Find two numbers that multiply to 50 and add up to 27. The numbers are 25 and 2 since $25\times2=50$ and $25 + 2=27$.

Step3: Rewrite middle term

Rewrite the middle - term $27x$ as $25x+2x$. So, $5x^{2}+27x + 10=5x^{2}+25x+2x + 10$.

Step4: Group terms

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

Step5: Factor out GCF from each group

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

Step6: Factor out common binomial

Factor out the common binomial $(x + 5)$: $5x(x + 5)+2(x + 5)=(5x + 2)(x + 5)$.

Answer:

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