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What is the completely factored form of the expression [tex][tex]$16x^2 + 8x + 32?$[/tex][/tex]

A. [tex]4\left(4x^2 + 2x + 8\right)[/tex]
B. [tex]4\left(12x^2 + 4x + 28\right)[/tex]
C. [tex]8\left(2x^2 + x + 4\right)[/tex]
D. [tex]8x\left(8x^2 + x + 24\right)[/tex]

Sagot :

GinnyAnsweridn
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]
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