To find the completely factored form of the expression [tex]\(16x^2 + 8x + 32\)[/tex], we should look for common factors and try to simplify the expression step-by-step.
1. Identify common factors among the coefficients of the terms in the expression:
[tex]\[
16x^2 + 8x + 32
\][/tex]
Notice that each term in the expression has a common factor of 8.
2. Factor out the greatest common factor (GCF), which is 8, from each term:
[tex]\[
16x^2 + 8x + 32 = 8(2x^2 + x + 4)
\][/tex]
3. After factoring out the 8, look at the expression inside the parentheses:
[tex]\[
2x^2 + x + 4
\][/tex]
Check if this quadratic trinomial can be factored further. In this case, [tex]\(2x^2 + x + 4\)[/tex] does not factor any further as a product of simpler linear binomials.
Thus, the completely factored form of the expression [tex]\(16x^2 + 8x + 32\)[/tex] is:
[tex]\[
8(2x^2 + x + 4)
\][/tex]
Among the given choices, the correct answer is:
[tex]\[
8(2x^2 + x + 4)
\][/tex]
