Remainder Theorem Practice

x - 7 x² - 7 x + 7 x² + 3x - 54

• x - 7

• x² - 7

• x + 7

• x² + 3x - 54

Given P(x) = 2x⁴ + x³ –3x² – x – 15. What is the value of P(2).

• 25

• 17

• 11

• 9

If f(x) = 5x² ─ 7x ─10, find the value of f (5) using synthetic division.

• 150

• 80

• 70

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

Answer explanation

To find the remainder when p(x) is divided by x - 2, evaluate p(2). Substituting x=2 into p(x) gives p(2) = -64. Therefore, the correct answer is p(2) = -64.

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

Let f(x) = 4x^2 -33x -27. Is x - 9 a factor of the function?

• yes

• no

Answer explanation

To check if x - 9 is a factor, substitute x = 9 into f(x). If f(9) = 0, then x - 9 is a factor. f(9) = 4(9)^2 - 33(9) - 27 = 0, so x - 9 is a factor.

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

• x + 1

• x + 2

• x + 5

• x + 10

Answer explanation

To find a factor of f(x), we can use synthetic division. By trying x + 1, we see that it divides evenly, indicating x + 1 is a factor.

Which binomial is a factor of
f(x)= x³ + x² -24x +36?

• x + 2

• x + 3

• x + 6

• x + 9

Answer explanation

To find a factor of f(x), we can use synthetic division. By dividing f(x) by x + 6, we get a remainder of 0, indicating x + 6 is a factor.

Decide if (x-3) is a factor of 3x³+10x²-x-12

• Yes, it is a factor!

• No, it is not a factor!

Answer explanation

(x-3) is not a factor of 3x^3+10x^2-x-12 because when you divide the polynomial by (x-3), you do not get a remainder of 0.