Question

4x2 is the GCF of this polynomial.

20x2y + 56x3 – ?
Which could be the mystery term?
A. 22x3
B. 24x2y
C. 26x2y
D. 28y3

Answer 1

option (B) is correct.

Mystery term has to be
`24x^2y`

Explanation:

Given :
`4x^2` is the GCF of the polynomial
`20x^2y + 56x^3 - ?`

We have to find the mystery term '?'

GCF stands for greatest common factor. GCF is the highest common factor that can divide all the given terms.

Here,
`4x^2` is the GCF of the polynomial
`20x^2y + 56x^3 - ?`

For unknown term , we have two conditions,

1) it has to be multiple of 4

2) it must have
`x^2` as a factor.

So out of given options only
`24x^2y` is a term which is both multiple of 4 and has
`x^2` as a factor.

Thus, Mystery term has to be
`24x^2y`

Thus, option (B) is correct.

Answer 2

Correct option is B

Explanation:

Note that

`20x^2y=2\cdot 2\cdot 5\cdot x\cdot x\cdot y,`

`56x^3=2\cdot 2\cdot 2\cdot 7\cdot x\cdot x\cdot x.`

If the mystery term is
`22x^3=2\cdot 11\cdot x\cdot x\cdot x,` then the

`GCF(20x^2y,56x^3,22x^3)=2\cdot x\cdot x=2x^2.`

If the mysteyr term is
`24x^2y=2\cdot 2\cdot 2\cdot 3\cdot x\cdot x\cdot y,` then

`GCF(20x^2y,56x^3,24x^2y)=2\cdot 2\cdot x\cdot x=4x^2.`

If the mysteyr term is
`26x^2y=2\cdot 13\cdot x\cdot x\cdot y,` then

`GCF(20x^2y,56x^3,26x^2y)=2\cdot x\cdot x=2x^2.`

If the mysteyr term is
`28y^3=2\cdot 2\cdot 7\cdot y\cdot y\cdot y,` then

`GCF(20x^2y,56x^3,28y^3)=2\cdot 2=4.`

Thus, correct option is B