question\nfactor.\n$x^{2}+14x + 45$
question\nfactor.\n$x^{2}+14x + 45$
Answer
Explanation:
Step1: Find two numbers
We need two numbers that multiply to 45 and add up to 14. The numbers are 9 and 5 since $9\times5 = 45$ and $9 + 5=14$.
Step2: Rewrite the middle - term
Rewrite $14x$ as $9x+5x$. So, $x^{2}+14x + 45=x^{2}+9x+5x + 45$.
Step3: Group the terms
Group the terms: $(x^{2}+9x)+(5x + 45)$.
Step4: Factor out the GCF from each group
Factor out the greatest - common factor (GCF) from each group. From $x^{2}+9x$, the GCF is $x$, so we get $x(x + 9)$. From $5x+45$, the GCF is 5, so we get $5(x + 9)$.
Step5: Factor out the common binomial factor
Factor out the common binomial factor $(x + 9)$: $x(x + 9)+5(x + 9)=(x + 5)(x + 9)$.
Answer:
$(x + 5)(x + 9)$