Remainder and Factor Theorem Practice Quiz

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.

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.

• Yes

• No

Answer explanation

Yes, x-1 is a factor of the polynomial because when the polynomial is divided by x-1, the remainder is 0.

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.

What is the remainder when      a³ - 4 is divided by a+2? 

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.

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

What is the remainder if

(x³ - 5x² + 2x - 10) is divided by (x - 5)?

• 0

• 4

• 7

• -1

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