Question

3a^4 + 11a
show your work here
hint: to add an exponent (x^y), type \exponent\ or press \^\.
o a(3a^3 + 11) o a(3a^6 + 33)
o 3a(3a^3 + 11) o a(3a^6 + 11)
factor the expression completely.
2z^2 + 8z + 8
show your work here
hint: to add an exponent (x^y), type \exponent\ or press \^\.
enter your answer

Explanation:

Step1: Factor out common factor for $3a^{4}+11a$

Find the greatest - common factor of $3a^{4}$ and $11a$. The GCF of the coefficients 3 and 11 is 1, and the GCF of the variable parts $a^{4}$ and $a$ is $a$. So, $3a^{4}+11a=a(3a^{3}+11)$.

Step2: Factor out common factor for $2z^{2}+8z + 8$

First, factor out the greatest - common factor of the coefficients 2, 8, and 8, which is 2. So, $2z^{2}+8z + 8=2(z^{2}+4z + 4)$.
Then, factor the quadratic expression $z^{2}+4z + 4$. Since $z^{2}+4z + 4=(z + 2)^{2}$ (using the formula $(x + y)^{2}=x^{2}+2xy+y^{2}$, where $x = z$ and $y = 2$), the fully - factored form is $2(z + 2)^{2}$.

Answer:

For $3a^{4}+11a$: A. $a(3a^{3}+11)$
For $2z^{2}+8z + 8$: $2(z + 2)^{2}$