Free Printable PRE-ASSESSMENT 2.2 The Remainder Theorem and Factor Theorem

Worksheets

PRE-ASSESSMENT 2.2 The Remainder Theorem and Factor Theorem

Total questions: 30

Worksheet time: 8hrs 30mins

Name

Class

Date

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

x + 1

x + 2

x + 5

x + 10

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

-2

-6

-12

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

x + 2

x + 3

x + 6

x + 9

Which binomial is a factor of
f(x)= 6x³ -35x² +34x +40?

2x - 3

2x - 5

3x - 2

5x - 2

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

-25

113

-113

What are the three factors for
(x³ -3x² -4x +12) ÷ (x + 2)?

(x-2) (x+2) (x+3)

(x-2) (x-2) (x+3)

(x+2) (x+2) (x+3)

(x-2) (x+2) (x-3)

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

-7

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

Which term is missing in this problem?
(2x³ + 5x² + 9) ÷
(x + 3)

x⁴

x³

x²

10.

If (x-2) is not a factor of (2x³-5x-7), what is the remainder?

-13

-1

11.

When (9x⁴- 45x³+ 37x² + x +2) is divided by (x-2), find the remainder.

656

652

-64

-368

12.

What is the remainder if

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

-1

13.

Which statement is true?

(x-3) is a factor of (x³- 3x²+ 2x + 2)

(x-3) is not a factor of (x³- 3x²+ 2x + 2)

The remainder when (x³- 3x²+ 2x + 2) is divided by (x-3) is zero.

The remainder when (x³- 3x²+ 2x + 2) is divided by (x-3) is not zero. The remainder is 17.

14.

Determine the remainder of (10x⁴- 50x³- 800) ÷ (x - 6).

-740

1,360

22,960

15.

If (2x²+10) is divided by (x -1), then what is the remainder?

-12

16.

Which expression will give a

remainder to the polynomial

(x³+ 9x²+ 23x + 15)

when the polynomial is divided by

the expression?

x + 5

x + 1

x + 3

x + 4

17.

What is a way to show that (x-5) is a factor of the polynomial

2x⁴- 3x³- 35x²- 9x + 45?

You can use synthetic division and show that the remainder is 10

You can use synthetic division and show that the remainder is zero

Multiply (x - 5) five times by itself.

There is no way to show that (x-5) is a factor of 2x⁴- 3x³- 35x²- 9x + 45.

18.

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

2x-10

-2x-10

2x+10

19.

Is (x-4) a factor of (x³ +x² -16x-16)?

YES

20.

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

Yes, it is a factor!

No, it is not a factor!

21.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

Yes

22.

Is (x-7) a factor of (x²-5x+14)?

Yes

23.

If P( -4) = 0, which of the following statements is true about P(x)?

x+4 is a factor of P(x)

P(x) = 0, has four negative roots

4 is a root of P(x) = 0

P(0) = - 4

24.

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

25.

(x – r) is a factor of P(x) if and only if __________.

P(r) ≠ 0

P(r) = 1

P(r) = 0

P(r) has two negative roots

26.

Is (y + 3) a factor of the polynomial: y³ - 6y + 9

yes

maybe

only on Tuesday's

27.

Determine if $\left(x-1\right)$ is a factor of $5x^4-2x^3+3x-6$ .

Yes

28.

What can we say if $P\left(-3\right)=0$ ?

$\left(x-3\right)\$ is a factor of $P\left(x\right)$

$\left(x+3\right)$ is a factor of $P\left(x\right)$

$\left(x-3\right)$ is NOT a factor of $P\left(x\right)$

29.

What can we say if $P\left(2\right)=3$ ?

$\left(x-2\right)$ is a factor of $P\left(x\right)$

$\left(x-2\right)$ is NOT a factor of $P\left(x\right)$

$\left(x+2\right)$ is NOT a factor of $P\left(x\right)$

30.

We know f(4) = 0 for f(x)= x³-6x²+5x+12. Factor f(x) completely using this information.

(x-4)(x+1)(x-3)

(x-4)(x+1)(x+3)

(x-1)(x-4)(x-3)

(x+1)(x+4)(x+3)

Reset

PRE-ASSESSMENT 2.2 The Remainder Theorem and Factor Theorem

Total questions: 30

Worksheet time: 8hrs 30mins

Similar Resources on Wayground