Question

FAN AND MEDAL




Part C: If the two middle terms were switched so that the expression became 3x3y - 9x2y + 12xy - 36y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning. (3 points)

Answer 1

@Nnesha

Answer 2

Part A: 3x^3y+12xy−9x^2y−36y

GCF of numbers = 3
GCF of y terms = y

3x^3y+12xy−9x^2y−36y


after factoring the 3 :
3(x^3y+4xy−3x^2y−12y)

after factoring the y :
3y(x^3+4x−3x^2−12)

Answer 3

Part B: 3y(x^3+4x−3x^2−12)

Factoring out GCF from first two terms gives :

3y(x(x^2+4)−3x^2−12)

3y(x^3+4x−3x^2−12)

Factoring out GCF from first two terms gives :
3y(x(x^2+4)−3x^2−12)

Factoring the GCF from last two terms gives :
3y(x(x^2+4)−3(x^2+4))

factoring out the (x^2+4) from the terms inside parenthesis gives :
3y(x^2+4)(x−3)