question\nfactor.\n$x^{2}+12x + 35$
question\nfactor.\n$x^{2}+12x + 35$
Answer
Explanation:
Step1: Find two numbers
We need two numbers that multiply to 35 and add up to 12. The numbers are 5 and 7 since $5\times7 = 35$ and $5 + 7=12$.
Step2: Rewrite the middle - term
Rewrite the quadratic expression $x^{2}+12x + 35$ as $x^{2}+5x+7x + 35$.
Step3: Group the terms
Group the terms: $(x^{2}+5x)+(7x + 35)$.
Step4: Factor out the GCF from each group
Factor out the greatest common factor (GCF) from each group. From $x^{2}+5x$, the GCF is $x$, so we get $x(x + 5)$. From $7x+35$, the GCF is 7, so we get $7(x + 5)$.
Step5: Factor out the common binomial factor
We have $x(x + 5)+7(x + 5)$. Factor out the common binomial factor $(x + 5)$ to get $(x + 5)(x+7)$.
Answer:
$(x + 5)(x + 7)$