Free Printable Test 4 Review: Polynomials, Binomial Expansion, Exponents

1.

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

2.

Which of the following are not polynomials? Check all that apply. (hint: polynomials can't have fractions as exponents, they can't have negative exponents and the variable can't be in the denominator.)

a)

$f\left(x\right)=2x^2+x^{\frac{1}{2}}-1$

b)

$g\left(x\right)=x^3\sqrt{10}+5x^{-2}+1$

c)

$t\left(x\right)=\pi x^4+\sqrt{6}$

d)

$j\left(x\right)=6-8x^3$

e)

$r\left(x\right)=8x^3-4x^2+\frac{2}{x}$

3.

A polynomial that has two terms is a:

a)

polynomial

b)

monomial

c)

binomial

4.

What is the term classification of the following polynomial?
x³-7x²+3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

5.

What is the degree of the polynomial
x²-2x+5

a)

1

b)

2

c)

3

d)

0

6.

Identify the constant term:
4x³ + 2x - 9

a)

4

b)

-2

c)

-9

d)

9

7.

How many terms does this expression have:
-27a³ + 9a² - 45a

a)

what are terms?

b)

0 terms

c)

-45 terms

d)

3 terms

8.

(3x + 4y - 3z) - (2x - 6y + 7z)

a)

x + 10y - 10z

b)

-x +10y - 10z

c)

x -10y - 10z

d)

-x -10y - 10z

9.

Add the polynomials.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

10.

Subtract: (2a² + 5a + 3) -(a² - 3a - 4)

a)

3a² + 2a - 1

b)

a²+ 8a + 7

c)

3a²+ 8a + 7

d)

a² + 2a - 1

11.

What is the perimeter of the rectangle?

a)

x²+8x-5

b)

2x²+16x-10

c)

2x²+10x-8

d)

6x-2

12.

(x + 5)(x + 4)

a)

x² + x + 20

b)

x² + 20x + 9

c)

x² + 9x + 20

d)

x² - 9x + 54

13.

Multiply the following together:

(2x + 3)(x² + 4x + 1)

a)

2x³ + 8x²+2x

b)

3x² + 12x +3

c)

2x³ +11x² +14x +3

d)

2x³ + 12x +3

14.

Find the product:

\left(5s+2\right)^2

a)

$25s^2+4$

b)

$25s^2+10s+4$

c)

$25s^2+20s+4$

d)

$5s^2+20s+4$

15.

$\left(m+5\right)\left(m^2+4m-8\right)$

a)

$m^3+4m^2-8m+5m^2+20m-40$

b)

$m^2+40m+m^3$

c)

$m^3+9m^2+12m-40$

16.

What is the area of this rectangle?

a)

48

b)

$8x^2+14x+6$

c)

$8x^2+x+5$

d)

$2x^2+6x+8$

17.

Find the product:

$\left(7r\ -\ 6\right)\left(7r\ +\ 6\right)$

a)

49r²+ 36

b)

49r²- 36

c)

49r²+ 84r + 36

d)

49r²+ 42r + 36

18.

Find the sum.
(3 - 2x + 2x²) + (4x - 5 + 3x²)

a)

7x - 7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x + 8

19.

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

20.

Simplify the expression
-6x - 5(10x + 3)

a)

-56x - 15

b)

-56x+15

c)

44x+15

d)

-44x-15

21.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

22.

(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

23.

Distribute and simplify

$x\left(3x^3+2x-5\right)$

a)

$3x^4+2x^2-5x$

b)

$3x^3+2x^2-5$

24.

Which of the following expression is equivalent to the given expression ?

a)

A

b)

B

c)

C

d)

D

25.

Which of the following expression is equivalent to the given expression ?

a)

A

b)

B

c)

C

d)

D

26.

Mary wants to subtract 3x² - 6x + 1 from
2x² - 3x - 4.
What is the correct set-up for this problem?

a)

(3x² - 6x + 1) - (2x² - 3x - 4)

b)

(2x² - 3x - 4) - (3x² - 6x + 1)

27.

Divide

$\frac{10x^8y^5}{4x^2y^5}$

a)

$6x^6y$

b)

$\frac{5x^6}{2}$

c)

$\frac{5x^6y}{2}$

d)

$6x^6$

28.

$\frac{20x^2}{5x}$

a)

$15x$

b)

$4x$

c)

$15x^2$

d)

$25x$

29.

What is a binomial?

a)

a polynomial of the sum or difference of two terms

b)

a polynomial of the sum or difference of two or more terms

c)

a polynomial of the sum of two terms

d)

a polynomial of the sum of two or more terms

30.

Choose the right Pascal's triangle

a)

b)

c)

d)

31.

Consider the binomial expansion of $\left(2y-5x\right)^6$ . How many terms are there in the expansion?

a)

6

b)

5

c)

7

d)

4

32.

Use the binomial expansion to expand $\left(u^2-2\right)^3$

a)

$u^6-6u^4+12u^2-8$

b)

$u^6-16u^4+12u^2-8$

c)

$5u^6-20u^4+40u^2-40$

d)

$u^6-24u^4+12u^2-8$

33.

What is the first term of $\left(2r-s\right)^8$

a)

$64r$

b)

$64r^8$

c)

$256r^8$

d)

$128r^8$

34.

What is the second term of $\left(3x-y\right)^5$

a)

$243x^2y^2$

b)

$-405x^4y$

c)

$243x^4$

d)

$81x^4y$

35.

Using $\left(2y-5x\right)^6$ , find the coefficient of the middle term of the expansion.

a)

20000

b)

-20000

c)

-21000

d)

-22000

36.

From $\left(x^2-2y\right)^7$ , find the fifth term.

a)

$566x^6y^4$

b)

$550x^6y^5$

c)

$560x^6y^4$

d)

$560x^4y^6$

37.

Consider the binomial expansion of $\left(3x^2-2y^3\right)^5$ . Find the third term of the expansion.

a)

$1080x^6y^6$

b)

$1180x^4y^5$

c)

$1088x^6y^4$

d)

$1011x^6y^6$

38.

Given the expression $\left(x^2-2y\right)^7$ . Use Binomial Theorem to find the coefficient of $x^{10}y^2$ .

a)

88

b)

74

c)

82

d)

84

39.

Find the coefficient of the term $x^8y^3$ of $\left(3x^2-2y^3\right)^5$

a)

-811

b)

-800

c)

-810

d)

-910

40.

Find the coefficient of $x^5$ in the expansion of $\left(2-x\right)\left(3x+1\right)^9$

a)

91854

b)

88547

c)

11238

d)

51030

41.

Select the correct expansion of

(1 - x)⁵

a)

1 − 5x + 10x² − 10x³ + 5x⁴ − x⁵

b)

1 + 5x + 10x² + 10x³ + 5x⁴ + x⁵

c)

-1 + 5x - 10x² + 10x³ - 5x⁴ + x⁵

d)

1 − 5x + 10x² + 10x³ + 5x⁴ − x⁵

42.

What is the Binomial expansion of (x + 1)⁵ ?

a)

x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

b)

x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

c)

x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

d)

x⁵ + 1

43.

Which row of Pascal's Triangle would you use to expand (x+y)³?

a)

1

b)

1 1

c)

1 2 1

d)

1 3 3 1

44.

How many terms are the in the expansion of (1+b)⁵

a)

5

b)

6

c)

25

d)

50

e)

3

45.

According to exponent rules, when we divide powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

46.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

47.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

48.

Rewrite using a positive exponent.
w^-13

a)

-w¹³

b)

¹/_w¹³

c)

¹/_w^-13

d)

w¹³

49.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

50.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

51.

Simplify the expression

a)

$\frac{-1}{3x^5y^7}$

b)

$3x^5y^7$

c)

$16x^{13}y^9$

d)

$\frac{1}{16x^{13}y^9}$

52.

$\left(2a^2\ b\right)\left(4ab^2\right)$

a)

$6a^2b^3$

b)

$6a^3b^2$

c)

$8a^3b^3$

d)

$8a^2b^2$

53.

$\left(2x^2y^3\right)^2$

a)

$2^2x^4y^5$

b)

$2x^4y^5$

c)

$4x^2y^5$

d)

$4x^4y^6$

54.

Any non-zero number raised to the zero

power is __________.

a)

0

b)

-1

c)

1

d)

100

55.

$\frac{18c^2}{-3c^3}$

a)

$\frac{6}{c}$

b)

$-6c^{ }$

c)

$\frac{-6}{c}$

d)

$\frac{18}{-3c}$

56.

\left(-2x^4\right)^{-2}

a)

$\frac{1}{-4x^8}$

b)

$\frac{1}{4x^8}$

c)

$-4x^{-6}$

d)

$4x^6$

57.

$\left(\frac{3m^2n^7}{m}\right)^5$

a)

$15m^7n^{12}$

b)

$243m^5n^{35}$

c)

$15m^{15}n^{35}$

d)

$243m^7n^{12}$

58.

$6x^5\cdot3x^5\cdot x^0$

a)

$9x^{10}$

b)

1

c)

0

d)

$18x^{10}$

59.

$\frac{x^{-2}}{x^{-10}y^{-8}}$

a)

$\frac{x^8}{y^{-8}}$

b)

$x^{20}y^8$

c)

$x^8y^8$

d)

$\frac{x^{10}y^8}{x^2}$

60.

a)

$25x^8y^2$

b)

$10x^8y^2$

c)

$-10x^2y^6$

d)

$25x^2y^8$

Test 4 Review: Polynomials, Binomial Expansion, Exponents

Total questions: 60

Worksheet time: 2hrs 44mins

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