Remainder Theorem for Polynomials

What is the remainder when p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x-2?

• 656

• 652

• -64

• -368

Find the remainder when 8x² - 5x + 1 is divided by x - 2

• -1

• 0

• 21

• 23

Answer explanation

Let p(x)= 8x² - 5x + 1 the zero of the polynomial x - 2 is 2 Evaluate p(2) p(2) = 8(2)² -5(2) + 1 = 32 - 10 + 1 = 23 So, by the Remainder Theorem, 23 is the remainder when 8x² - 5x + 1 is divided by x - 2 Alternatively, we can do the long division. When we divide 8x² - 5x + 1 by x - 2, we get 23 as the remainder Hence, option 4 is the correct answer.

What is the remainder?

(3x³ + 5x - 1) ÷ (x + 1)

• -2

• -9

• 7

• 0

If (x²+3x+7) is divided by (x+2), then what is the remainder?

• 0

• -3

• 9

• 5

The remainder when (x3 - px2 - p) is divided by (x - p)

• p

• -p

• 5p

• -5p

• -1

• 102

• 0

• 100

Given f(x) = -x² - x + 20 and it is divided by (x + 4) Use the Remainder Theorem to find the Remainder for f(x) f(x) = -(___)² - (___) + 20

Use the Remainder Theorem to evaluate f(x) = 2x² − 4x³ + 5x² − 9x at c = -1.

Mathematical Equivalence

ON

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

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