Remainder Theorem to Evaluate

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

Using the remainder theorem, which of the below is a true statement?

• f(12) = 1

• f(1) = 12

• (x+1) is a root

• (x-1) is a root

Determine the remainder if the polynomial is divided by the binomial (Apply Remainder Theorem).

• 0
  

• -6

• -8

• -10

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

Mathematical Equivalence

ON

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.

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

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

Determine if the binomial is a factor of the polynomial. (Apply Remainder Theorem)
\left(3n^3-26n^2-39n-10\right)\div\left(n-10\right)

• Yes

• No