Question

which of the following is not an equivalent way to write the binomial $24x^2 + 16x$ in factored form?
(1) $x(24x + 16)$
(2) $8x(3x + 2)$
(3) $12x(2x + 4)$
(4) $4(6x^2 + 4x)$

Explanation:

Step1: Expand each option

• For option (1): $x(24x + 16)=24x^2+16x$ (using distributive property $a(b + c)=ab+ac$)
• For option (2): $8x(3x + 2)=8x\times3x+8x\times2 = 24x^2+16x$
• For option (3): $12x(2x + 4)=12x\times2x+12x\times4=24x^2 + 48x$
• For option (4): $4(6x^2+4x)=4\times6x^2+4\times4x = 24x^2+16x$

Step2: Compare with original binomial

The original binomial is $24x^2 + 16x$. We see that option (3) expands to $24x^2+48x$ which is not equal to the original binomial.

Answer:

(3) $12x(2x + 4)$