Question 1 : Dorian factors the polynomial P(x)=8x3+20x2−18x−45. His work is shown below.

Line 1: P(x)=8x^3+20x^2−18x−45
Line 2: =(8x^3+20x^2)+(−18x−45)
Line 3: =4x^2(2x+5)−9(2x+5)
Line 4: =(4x2−9)(2x+5)2
Line 5: =(2x+3)(2x−3)(2x+5)2

When Dorian double checks his answer, he finds that it is incorrect. In which line did Dorian first make a mistake?

a. Line 1
b. Line 5
c .Line 2
d. Line 4
e .Line 3

Question 2: Consider the polynomial p(x)=32x5^y−2xy^5.

Part A: What is the complete factorization of p(x)=32x5^y−2xy^5 over the integers?

Part B: What methods are used to factor p(x)=32x^5y−2xy^5?

Select one answer for Part A and select all answers that apply for Part B.

A: 2xy(2x−y)(2x+y)(4x2+y2)
A: 2xy(4x^2−y^2)(x^4−4x^2y^2+y^4)
B: greatest common factor
A: 2xy(2x−y)^2(2x+y)^2
B: grouping
B: repeated difference of squares
B: difference of cubes