Dividing Polynomials with Remainders

The Remainder Theorem states that when a polynomial f(x) is divided by (x-c), the remainder is:

• F'(C)

• C^2

• f(c)

• Zero

What is the purpose of synthetic division?

• To divide two polynomials quickly, especially when the divisor is linear

• To find the square root of a polynomial expressions

• To simplify polynomials into factored form

• To multiply two polynomials

In synthetic division, what does the final value in the row represent?

• The quotient of the division

• The remainder of the division

• The degree of the polynomial

• The divisor

2x³ - 5x² + 3x + 7 ÷ x - 2

• 2x³ - x² + x + 9

• 2x² - x + 1

• 2x² - x + 1 + 9/(x - 2)

• 2x² - 9x - 15 - 23/(x - 2)

• This is correct
• This is incorrect

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³ - 5x² + 2x - 10

• 0

• 2x-10

• -2x-10

• 2x+10

When p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

• p(2) = 656

• p(2) = 652

• p(2) = -64

• p(2) = -368

• This is correct
• This is incorrect

Divide using synthetic division

(2x³ + 4x² - 5) by (x + 3).

• 2x² + 2x - 4 - 12/(x + 3)

• 2x² - 2x + 6 - 23/(x + 3)

• 2x² - 2x + 8 - 20/(x + 3)

• 2x² - 4x + 1