Question 1: The polynomial P(x)=x^3−6x^2+6x−23 can be rewritten as P(x)=(x^2+6)(x−6)+13.

Which expression is a factor of P(x)?

a. x^2+6

b. x−6

c. 13

d. none of these

Question 2: Petra is practicing factoring by grouping. She wants to factor the polynomial 16xy−4x^2+28y−7x. Her work is shown below.

16xy−4x^2+28y−7x
4x(4y−x)+7(4y−x)
(4x+7)(4y−x)

Which statements regarding Petra’s work are true?

There may be more than one correct answer. Select all correct answers.

1. The constant 7 is not the greatest common factor of 28y−7x.

2. Petra is correct.

3. The product of Petra’s factors is not the original polynomial.

4. The monomial 4x is not the greatest common factor of 16xy−4x^2.

5. Petra is incorrect.

6. The product of Petra’s factors is the original polynomial.