Verified Answer :

W0lf93

We can give 8 as a common factor and write in parantheses what remains of each term after dividing it by 8. So we have 16x^2 + 8x + 32 = 8*(2x^2 + x + 4). So the answer is C.

Answer:

\(8(2x^2+x+4)\)

Step-by-step explanation:

Given expression,

\(16x^2 + 8x + 32\)

Since,

16 = 2 × 2 × 2 × 2,

8 = 2 × 2 × 2

32 = 2 × 2 × 2 × 2 × 2

LCM(16, 8, 32) = 2 × 2 × 2 = 8,

\(\implies 16x^2+8x+32 = 8(2x^2 + x + 4)\)

Now, \(1^2 - 4\times 2 \times 4 eq 0\)

⇒ \(2x^2 + x + 4\) is not a perfect square trinomial,

Hence, the completely factored form of the given expression is,

\(8(2x^2 + x+4)\)

i.e. THIRD option is correct.

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