Question

Jill is factoring the expression 13xy-52y. Her work is shown below.

Factors of 13xy: 1, 13, x, y
Factors of 52y: 1, 2, 26, 52, y
GCF: y Factored expression: y(13x-52)

Which best describes the accuracy of Jill’s solution?

Jill’s solution is accurate.

Jill omitted a factor pair, which affected the GCF and factored expression.

Jill made an error when determining the GCF from her list of factors.

Jill made an error when writing the factored expression.

Answer 1

Jill omitted a factor pair , which affected the GCF and factored expression.

Explanation:

Jill's expression

13xy-52y

Factor of 13xy: 1,13,x,y

Factore of 52y: 1,2,26,52,13,4,y

But Jill give factor of 52y: 1,2,26,52,y

Jill make a mistake when Jill factorise 52y .

He does not take 13 and 4 in his factor.

GCF :
`13xy=13* x* y`

`52y= 13* 4* y`

The common factor of both terms are 13 and y

Therefore, GCF:
`13* y =13y`

But Jill give GCF:y

Jill give factored expression : y(13x-52)

But actual factored expression: 13y(x-4)

Therefore , Jill omitted a factor pair which affect the GCF and factored expression .

Answer 2

Jill omitted a factor pair, which affected the GCF and factored expression.

Factors of 52y: 1, 2, 26, 52, y she also needs to include 13*4