Question

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

A. 3x - 2
B. 3x - 1
C. 3x + 1
D. 3x + 2
​

Answer 1

A. 3x - 2

Explanation:

`(6x^2)/(2x)=3x,\ (-3x)/(-1)=3x\\\\(-4x)/(2x)=-2,\ (2)/(-1)=-2\\\\\underline\ \ 2x\ \\\underline\ 6x^2\ \\.\ -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}`

Answer 2

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)