Remainder and Remainder Theorem

• True

• False

Complete the synthetic division and use the remainder to determine a true statement concerning p(x) and its solutions.

• -2 is a solution of p(x) since the remainder is equal to 0.

• -2 is not a solution of p(x) since the remainder is equal to 1.

• -2 is not a solution of p(x) since the remainder is equal to 33.

• 2 is not a solution of p(x) since the remainder is equal to -1.

Based on the remainder you found, which statement is true?

Assume that x-2 is a factor of a polynomial. Which x-value must be a solution of that same polynomial?

• The x-value -2

• The x-value 2

• The x-value 0

Finish dividing p(x)=5x^3+34x^2+26x+C by x+6. Determine what value C must equal if x+6 is a factor of p(x).

• C would need to be equal to 0.

• C would need to be equal to 12.

• C would need to be equal to -12.

• C would need to be equal to 300.

What is the remainder when (10x⁷⁹ – 6) is divided by (x-1)?

• 4

• 3

• 2

• 1

Given (2x³ – 2x² + x + 4) divided by x – 4, what is the remainder?

• 111

• 107

• 104

• 84

x – r is a factor of P(x) if and only if the remainder R of P(x) ÷ (x-r) is ______.

What is the remainder when ( 2x⁵⁰ – 5) is divided by (x-1)?

• 8

• 5

• -5

• -3

Which polynomial when divided by (x - 2) equals (x² – x – 3) with a remainder of -3 ?

• x³ + 3x² – x + 3

• x³ – 3x² + x + 3

• x³ – x² – x + 3

• x³ – 3x² – x + 3