## Question 1 : Dorian factors the polynomial P(x)=8×3+20×2−18x−45. His work is shown below. Line 1: P(x)=8x^3+20x^2−18x−45 L

Question 1 : Dorian factors the polynomial P(x)=8×3+20×2−18x−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: =(4×2−9)(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)=32×5^y−2xy^5.

Part A: What is the complete factorization of p(x)=32×5^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)(4×2+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

## Answers ( )

Answer:Problem #1: Option D, Line 4

Problem #2

PART A: Option 1, 2xy(2x−y)(2x+y)(4×2+y2)

PART B: Option 3, greatest common factor, Option 6, repeated difference of squares

Step-by-step explanation:Problem #1Step 1: Factor P(x) = 8x^3 + 20x^2 − 18x − 45

4x^2(2x + 5) – 9(2x + 5)

(4x^2 – 9)(2x + 5)

(2x + 3)(2x – 3)(2x + 5)Answer:

Option D, Line 4Problem #2Part A: Factor2xy(16x^4 – y^4)

2xy(4x^2 + y^2)(2x + y)(2x – y)

Answer:

Option 1, 2xy(2x−y)(2x+y)(4×2+y2)Part B: Find the methods

Option 3, greatest common factorOption 6, repeated difference of squares