Question

fully factor the expression.
3r² + 8r + 4
show your work here
(3r + 14)(r + 2) (12r + 2)(r + 2)
(3r + 2)(r + 2) (6r + 2)(r + 2)
factor the polynomial below.
25b² - 80b + 64
show your work here
hint: to add an exponent (x^y), type \exponent\ or press \^\.
enter your answer

Explanation:

Step1: Factor $3r^{2}+8r + 4$

For a quadratic $ax^{2}+bx + c$ (here $a = 3$, $b=8$, $c = 4$), we need to find two numbers that multiply to $ac=3\times4 = 12$ and add up to $b = 8$. The numbers are $6$ and $2$. So we rewrite the middle - term: $3r^{2}+6r+2r + 4$.

Step2: Group the terms

Group the terms as $(3r^{2}+6r)+(2r + 4)$. Factor out the greatest common factor from each group: $3r(r + 2)+2(r + 2)$.

Step3: Factor out the common binomial

Factor out $(r + 2)$ to get $(3r + 2)(r + 2)$.

Step4: Factor $25b^{2}-80b + 64$

This is in the form of a perfect - square trinomial $a^{2}-2ab + b^{2}=(a - b)^{2}$, where $a = 5b$ (since $(5b)^{2}=25b^{2}$) and $b = 8$ (since $2\times5b\times8=80b$ and $8^{2}=64$). So $25b^{2}-80b + 64=(5b - 8)^{2}$.

Answer:

1. $(3r + 2)(r + 2)$
2. $(5b - 8)^{2}$