what is the completely factored form of the expression $16x^2 + 8x + 32$?\n$\\bigcirc\\ 4(4x^2 + 2x +…

what is the completely factored form of the expression $16x^2 + 8x + 32$?\n$\\bigcirc\\ 4(4x^2 + 2x + 8)$\n$\\bigcirc\\ 4(12x^2 + 4x + 28)$\n$\\bigcirc\\ 8(2x^2 + x + 4)$\n$\\bigcirc\\ 8x(8x^2 + x + 24)$

what is the completely factored form of the expression $16x^2 + 8x + 32$?\n$\\bigcirc\\ 4(4x^2 + 2x + 8)$\n$\\bigcirc\\ 4(12x^2 + 4x + 28)$\n$\\bigcirc\\ 8(2x^2 + x + 4)$\n$\\bigcirc\\ 8x(8x^2 + x + 24)$

Answer

Explanation:

Step1: Find GCF of coefficients

The coefficients are 16, 8, 32. GCF of 16, 8, 32 is 8.

Step2: Factor out GCF

Factor out 8 from (16x^{2}+8x + 32):
(8\times\frac{16x^{2}}{8}+8\times\frac{8x}{8}+8\times\frac{32}{8}=8(2x^{2}+x + 4))
Check other options:

  • (4(4x^{2}+2x + 8)): GCF here is 4, but 8 is a higher GCF.
  • (4(12x^{2}+4x + 28)): Incorrect expansion (12x²≠16x²/4).
  • (8x(8x^{2}+x + 24)): Incorrect (extra x factor, expansion wrong).

Answer:

8(2x² + x + 4) (the third option: 8(2x² + x + 4))