Monique is factoring the expression 4x + 16xy. Her work is shown below. Factors of 4x: 1,2,4,x
Factors of 16xy: 1, 2, 4, 8, 16, x, y
GCF: 4x
Factored expression: 4x(0 + 4y)

Which best describes the accuracy of Monique's solution?

A. Monique's solution is accurate.
B. Monique made an error when listening the factors, which affected the GCF and the factors expression.
C. Monique made an error when determining the GCF from her list of factors.
D. Monique made and error when writing the factored expression.

D

Step-by-step explanation:

She made an error writing the expression

it should be 4(x + 4y)

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

my dear correct answer is option number 3