Question

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

Explanation:

Step1: Find GCF of terms

Find GCF of \(8x^2\) and \(12x\). Prime factors: \(8x^2 = 2^3 \cdot x^2\), \(12x = 2^2 \cdot 3 \cdot x\). GCF is \(2^2 \cdot x = 4x\).

Step2: Factor out GCF

Factor \(4x\) from \(8x^2 + 12x\): \(4x(2x + 3)\) (since \(8x^2\div4x = 2x\), \(12x\div4x = 3\)).

Step3: Verify options

Check other options:

• \(4(4x^2 + 8x)\) expands to \(16x^2 + 32x

eq 8x^2 + 12x\).

• \(8x(x + 4)\) expands to \(8x^2 + 32x

eq 8x^2 + 12x\).

• \(8x(x^2 + 4)\) expands to \(8x^3 + 32x

eq 8x^2 + 12x\).

Only \(4x(2x + 3)\) matches.

Answer:

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