## Question 1: Monica wants to find the greatest common factor of the terms of the polynomial p(x)=12×3^y+6xy^2+18xy+24x. She sees that each te

Question 1: Monica wants to find the greatest common factor of the terms of the polynomial p(x)=12×3^y+6xy^2+18xy+24x. She sees that each term is divisible by 3x. She factors the polynomial as follows:

3x(4x^2y+2y^2+6y+8)

Did Monica correctly factor out the greatest common factor? Why or why not?

a. Monica is incorrect, the GCF should only include constants.

b. Monica is correct, 3x is the GCF and she factored it out correctly.

c. Monica is incorrect, the GCF should only include variables.

d. Monica is incorrect, there is a common factor larger than 3x.

Question 2: Lana uses factoring by grouping to factor the polynomial 8x^2y−10xy^2+12x−15y. Her work is shown below, but the last two lines of work are missing.

8x^2y−10xy^2+12x−15y

(8x^2y−10xy^2)+(12x−15y)

__[blank 1]__

__[blank 2]__

Select one statement for each blank to correctly complete Lana’s work.

a. blank 1: 2xy(4x−5y)+3(4x−5y)

a. blank 2: (2xy−3)(4x+5y)

b. blank 2: (2xy+3)(4x−5y)

b. blank 1: −2xy(4x+5y)−3(4x+5y)

c. blank 1: −4x(2xy+3)+5y(2xy+3)

c. blank 2: −(2xy+3)(4x−5y)

## Answers ( )

Answer:Question 1: Option D, Monica is incorrect, there is a common factor larger than 3x.

Question 2:

Option 1, a. blank 1: 2xy(4x−5y)+3(4x−5y)

Option 3, b. blank 2: (2xy+3)(4x−5y)

Step-by-step explanation:Question 1Step 1: Find the greatest common factorp(x) = 12x^3y + 6xy^2 + 18xy + 24x

p(x) = 3x(4x^2y + 2y^2 + 6y + 8)Answer:

Option D, Monica is incorrect, there is a common factor larger than 3x.Question 2Step 1: Factor8x^2y − 10xy^2 + 12x − 15y

(8x^2y − 10xy^2) + (12x − 15y)

2xy(4x – 5y) + 3(4x – 5y)(2xy + 3)(4x – 5y)Answer:

Option 1, a. blank 1: 2xy(4x−5y)+3(4x−5y)Option 3, b. blank 2: (2xy+3)(4x−5y)