what is the factored form of $8x^{2}+12x$?\n$4(4x^{2}+8x)$\n$4x(2x + 3)$\n$8x(x + 4)$\n$8x(x^{2}+4)$

Answer:

B. (4x(2x + 3))

Explanation:

Step1: Find the greatest common factor (GCF)

For (8x^{2}) and (12x), the GCF of (8) and (12) is (4), and the GCF of (x^{2}) and (x) is (x). So the GCF is (4x).

Step2: Factor out the GCF

[ \begin{align*} 8x^{2}+12x&=4x\times2x + 4x\times3\ &=4x(2x + 3) \end{align*} ] Check other options:

• Option A: (4(4x^{2}+8x)=16x^{2}+32x\neq8x^{2}+12x)
• Option C: (8x(x + 4)=8x^{2}+32x\neq8x^{2}+12x)
• Option D: (8x(x^{2}+4)=8x^{3}+32x\neq8x^{2}+12x)