Free Printable Chapter 3 Test Review Polynomials

1.

The following polynomial is written in standard form:
7x³ - 11x² + 8x - 5

a)

True

b)

False

2.

Which of these is in Standard Form?

a)

$4x^2+12x-13x^3$

b)

$5-3x$

c)

$2x^4-12x^2+5x-9$

d)

$5x^5+4x^{\text{4}}+12x^3-23x+15$

3.

Which polynomial is written in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

4.

What is the constant in the polynomial x²-2x+5?

a)

1

b)

2

c)

5

d)

0

5.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

-2x⁵ + 3x - 1

b)

5x^-2 +3x - 1

c)

-2x⁵ + 3x⁴ + 2x³ + x² - 10

d)

2x + 5

6.

What is the leading coefficient in the polynomial 3x²-2x+5?

a)

3

b)

2

c)

5

d)

0

7.

Classify by the DEGREE:
4x³ - 5x² + 2x - 1

a)

Degree of 1

b)

Degree of 2

c)

Degree of 3

d)

Degree of 4

8.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

9.

(4a + 2)(6a² − a + 2)

a)

24a³ + 16a² + 6a + 4

b)

24a³ + 8a² + 10a + 4

c)

24a³ + 8a² + 6a + 4

d)

24a³ - 8a² - 6a + 4

10.

What does multiplicity of a zero mean?

a)

Look at the number of terms

b)

How many times the zero repeats

c)

Find the sum of all the coefficients

d)

Ratio your x and y

11.

What is the quotient when (3x³ + 5x - 1) is divided by (x + 1)?

a)

$3x^3-3x^2+8x-9$

b)

$3x^2-3x+8-\frac{9}{x+1}$

c)

$3x^2+3x+8+\frac{7}{x+1}$

d)

$3x^3+3x+8+\frac{7}{x+1}$

12.

Given the polynomial 4x² -33x -27.

Is k = 9 a zero of the function?

a)

Yes, the remainder is 0

b)

No, the remainder is 0

c)

Yes, the remainder is 12

d)

No, the remainder is 12

13.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

14.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x - 2) using synthetic division. His work is shown above.

Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

15.

Is (x-2) a factor of

f(x)= x³- 8x²+ 14x - 4 ?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

16.

Add to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

17.

Add or Subtract to Simplify:
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

18.

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

a)

-25

b)

25

c)

113

d)

-113

19.

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

a)

P(a) ≠ 0

b)

P(a) = 1

c)

P(a) = 0

d)

P(a) has two negative roots

20.

Find the remainder when

P\left(x\right)=x^4+x^3-2x^2+4x-5

is divided by

\left(x+3\right)

.

a)

19

b)

20

c)

21

d)

22

21.

Identify the following polynomial.
$36x^2-y^2$

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

22.

Identify the following polynomial.
$1-a^3$

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

23.

Identify the "a" and "b" values of the following polynomial.
$a^3+343b^3$

a)

$a:\ a$ $b:\ 7b$

b)

$a:\ a$ $b:\ 7$

c)

$a:\ a^3$ $b:\ b^3$

d)

$a:\ a$ $b:\ 343b$

24.

Factor

x³-64

a)

(x-4)(x²+4x+16)

b)

(x-4)(x²-4x+16)

c)

(x+4)(x²-4x+16)

d)

(x+4)(x²+4x+16)

25.

x³ - 27

a)

(x - 4)(x² + 4x + 16)

b)

(x + 3)(x² - 4x + 16)

c)

(x - 1)(x² + 1x + 1)

d)

(x - 3)(x² + 3x + 9)

26.

Select the coefficients of the 5th Row in Pascal's Triangle

a)

1;3;3;1

b)

1;4;6;4;1

c)

1;5;10;10;5;1

d)

1;6;15;20;15;6;1

27.

Expand the expression using the Binomial Theorem.

(2x+5)⁴

a)

2x⁴ + 40x³+ 300x² + 1000x +625

b)

16x⁴+ 160x³ +600x² +1000x + 625

c)

16x⁴ + 1000x³ + 600x²+ 160x +625

28.

Expand (d-5)⁵

a)

d⁵ - 25 d⁴ + 250 d³ - 1250 d² + 3125 d - 3125

b)

d⁵ + 25 d⁴ + 250 d³ + 1250 d² + 3125 d + 3125

c)

d⁴- 20d³+ 150d²- 750d + 3125

d)

d⁴+ 20d³+ 150d²+ 750d + 3125

29.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

30.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

31.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

a)

±1, ±5, ±1/2, ±5/2

b)

±1, ±2, ±5, ±1/2, ±5/2

c)

±1, ±5

d)

±1, ±2, ±5, ±1/2, ±5/2, ±2/5

32.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

33.

The two parts of the equation that determine the end behavior are...(select both)

a)

Degree (even/odd)

b)

Leading coefficient (positive/negative)

c)

X-intercepts (positive/negative)

d)

Number of terms (even/odd)

34.

What is the degree?

a)

Odd

b)

Even

35.

Is this polynomial odd, even, or neither?

5x³ - 6x + 1

a)

Odd

b)

Even

c)

Neither

Chapter 3 Test Review Polynomials

Total questions: 35

Worksheet time: 9hrs 45mins

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