Question

The diagram represents 6x^2 - 7x + 2 with a factor of 2x - 1. What is the other factor of 6x^2 - 7x + 2?

Answer 1

Answer:

 A. 3x - 2

Step-by-step explanation:

To find the factors on the left hand side of the table, factor out common factor from each row

GCF of 6x^2 and -3x

$6x^2= 3 \cdot 2 \cdot x \cdot x$

$-3x= -3 \cdot x$

GCF is 3x

GCF of -4x and 2

$-4x= -2 \cdot 2 \cdot x$

GCF is -2. Take out negative to make the first term positive.

So other factor is (3x-2)

Answer 2

Answer:

A. 3x - 2

Step-by-step explanation:

$\dfrac{6x^2}{2x}=3x,\ \dfrac{-3x}{-1}=3x\\\\\dfrac{-4x}{2x}=-2,\ \dfrac{2}{-1}=-2\\\\\underline{.\qquad|\ \ 2x\ |\ -1\ |}\\\underline{.\ 3x\ \ |\ 6x^2\ |-3x|}\\.\ -2|-4x|\ \ 2\ \ |$

$\text{Check:}\\\\(2x-1)(3x-2)=(2x)(3x)+(2x)(-2)+(-1)(3x)+(-1)(-2)\\\\=6x^2-4x-3x+2=6x^2-7x+2\qquad\text{CORRECT}$