Question

1. which function is equivalent to $f(x)=6x^{2}-13x + 5$?

$f(x)=(3x - 1)(x - 5)$
$f(x)=(3x - 5)(2x - 1)$
$f(x)=(3x - 5)(2x + 1)$
$f(x)=(3x - 1)(2x + 5)$
clear all

Explanation:

Step1: Expand option A

$$\begin{align*} (3x-1)(x-5)&=3x\cdot x - 3x\cdot5 -1\cdot x +1\cdot5\\ &=3x^2-15x-x+5\\ &=3x^2-16x+5 \end{align*}$$

Step2: Expand option B

$$\begin{align*} (3x-5)(2x-1)&=3x\cdot2x -3x\cdot1 -5\cdot2x +5\cdot1\\ &=6x^2-3x-10x+5\\ &=6x^2-13x+5 \end{align*}$$

Step3: Verify matches original function

The expanded result of option B matches $f(x)=6x^2-13x+5$.

Answer:

B. $f(x)=(3x - 5)(2x - 1)$