Free Printable Alg 2 - 5.1, 5.3, 5.5 Review (2021-2022)

1.

$a^6$ $a\cdot a^2\cdot a^3$

a)

$a^{12}$

b)

$a^{-6}$

c)

$\frac{1}{a^6}$

d)

$6a^5$

2.

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

a)

$6a^2b^3$

b)

$6a^3b^2$

c)

$8a^3b^3$

d)

$8a^2b^2$

3.

When you have a power to a power you __________________________________ the exponents.

a)

Divide

b)

Multiply

c)

Add

d)

Subtract

4.

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

a)

$2^2x^4y^5$

b)

$2x^4y^5$

c)

$4x^2y^5$

d)

$4x^4y^6$

5.

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

a)

$\frac{6}{c}$

b)

$-6c^{ }$

c)

$\frac{-6}{c}$

d)

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

6.

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

a)

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

b)

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

c)

$-4x^{-6}$

d)

$4x^6$

7.

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

a)

$15m^7n^{12}$

b)

$243m^5n^{35}$

c)

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

d)

$243m^7n^{12}$

8.

To turn a negative exponent positive you

______________________.

a)

Multiplying

b)

Change the negative to positive

c)

Flip it

d)

Adding

9.

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

a)

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

b)

$x^{20}y^8$

c)

$x^8y^8$

d)

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

10.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

11.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

12.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

13.

a)

b)

c)

d)

14.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

15.

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

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

16.

Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

17.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

18.

Multiply:

(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

19.

Multiply:

(b + 3) (b²+ 2b + 1)

a)

b³+ 6b²+ 6b + 3

b)

b³+ 5b²+ 7b + 3

c)

4b³+ 8b²+ 3b

d)

3b³+ 6b²+ 3b

20.

Multiply:

(x + 1) (x - 6) (x + 4)

a)

x³ - x² - 26x - 24

b)

x³ - 9x² - 14x - 24

c)

x³ - 11x² - 24x - 24

d)

x² - 5x - 6

21.

6v(2v + 3)

a)

12v+18

b)

15v² + 8v

c)

12v² + 18v

d)

12v² + 18v²

22.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

23.

Multiply
(x+5)²

a)

x²+25

b)

x²-25

c)

x²+10x+25

d)

x²-10x+25

24.

Multiply
(x²-2x+1)(x+1)

a)

x³-x²-x+1

b)

x³-2x+2

c)

x³+x²+x+1

d)

x³-3x²-3x+1

25.

Multiply: (−8k² −3k−1)(3k² −k+6)

a)

−20k⁴ −k³ −45k² −17k−1

b)

−24k⁴ −k³ −48k² −17k−6

c)

−24k³−k³ −48k² −17k−6

d)

−24k⁴ −k³ −48k²

26.

Multiply: (6x² +x+1)(−6x² −6x−8)

a)

−6x⁴ −7x³−6x² −7x−8

b)

36x⁴ −42x³−60x² + 14x + 8

c)

−36x⁴ −42x³−60x² −14x−8

27.

Divide Using Long Division:

(10x⁴+4x³-8x²+3x+10) / (2x²-4x)

a)

5x²+12x+20+((83x+10)/(2x²-4x))

b)

5x²+12x+20

c)

10x⁴+3x+10

d)

7x⁴+11x³+102x²+30x+22+(83 / 2x²-4x)

28.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

29.

Divide using long division. $\left(x^2-3x-40\right)\div\left(x+5\right)$

a)

$\left(x+5\right)\left(x-8\right)$

b)

$\left(x+5\right)\left(x+8\right)$

c)

$\left(x+5\right)\left(x-6\right)$

d)

$\left(x+5\right)\left(x+6\right)$

30.

Divide using long division. $\left(9x^3-18x^2-x+2\right)\div\left(3x+1\right)$

a)

$\left(3x+1\right)\left(3x^2-7x+2\right)$

b)

$\left(3x+1\right)\left(x-6\right)\left(x-1\right)$

c)

$\left(3x+1\right)\left(x+2\right)\left(3x+1\right)$

d)

$\left(3x+1\right)\left(x-2\right)\left(3x-1\right)$

31.

Divide using long division. $\left(2x^3+9x^2+14x+5\right)\div\left(2x+1\right)$

a)

$\left(2x+1\right)\left(x^2-6x+10\right)$

b)

$\left(2x+1\right)\left(x^2-4x+8\right)$

c)

$\left(2x+1\right)\left(x^2+4x+5\right)$

d)

$\left(2x+1\right)\left(x^2+4x-5\right)$

32.

Divide using long division. $\left(x^4+3x^2+x+4\right)\div\left(x+3\right)$

a)

$x^3-3x^2+12x-35+\frac{109}{x+3}$

b)

$x^3+3x^2-12x-35+\frac{109}{x+3}$

c)

$x^3-3x^2-12x+30-\frac{109}{x+3}$

d)

$x^3+3x^2+10x-15+\frac{109}{x+3}$

33.

Divide using long division. $\left(x^5+1\right)\div\left(x+1\right)$

a)

$\left(x+1\right)\left(x^4-x^2+1\right)$

b)

$\left(x+1\right)\left(x^4+x^3-x^2+x-1\right)$

c)

$\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)$

d)

$\left(x+1\right)\left(x^4-x^3-x-1\right)$

34.

Divide using synthetic division. $\left(x^2-3x-40\right)\div\left(x+5\right)$

a)

$\left(x+5\right)\left(x-8\right)$

b)

$\left(x+5\right)\left(x+8\right)$

c)

$\left(x+5\right)\left(x-6\right)$

d)

$\left(x+5\right)\left(x+6\right)$

35.

Divide using long division. $\left(3x^2+7x-20\right)\div\left(x+4\right)$

a)

$\left(x+4\right)\left(3x+5\right)$

b)

$\left(x+4\right)\left(3x+25\right)$

c)

$\left(x+4\right)\left(3x-5\right)$

d)

$\left(x+4\right)\left(3x-10\right)$

36.

Divide using synthetic division. $\left(x^3+3x^2-x+2\right)\div\left(x-1\right)$

a)

$x^2+4x+3-\frac{5}{x-1}$

b)

$x^2+4x+3+\frac{5}{x-1}$

c)

$x^2-4x+3+\frac{5}{x-1}$

d)

$x^2-4x-3-\frac{5}{x-1}$

37.

Divide using synthetic division. $\left(2x^3-3x^2-18x-8\right)\div\left(x-4\right)$

a)

$\left(x-4\right)\left(x+2\right)\left(2x+1\right)$

b)

$\left(x-4\right)\left(x-2\right)\left(2x-1\right)$

c)

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

d)

$\left(x-4\right)\left(x+4\right)\left(x+1\right)$

38.

Divide using synthetic division. $\left(x^3-13x-12\right)\div\left(x-4\right)$

a)

$\left(x-4\right)\left(x^2+4x+3\right)$

b)

$\left(x-4\right)\left(x+3\right)\left(x+1\right)$

c)

$\left(x-4\right)\left(x+3\right)\left(x-1\right)$

d)

$\left(x-4\right)\left(x-3\right)\left(x-1\right)$

39.

Divide using synthetic division. $\left(x^5+1\right)\div\left(x+1\right)$

a)

$\left(x+1\right)\left(x^4-x^2+1\right)$

b)

$\left(x+1\right)\left(x^4+x^3-x^2+x-1\right)$

c)

$\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)$

d)

$\left(x+1\right)\left(x^4-x^3-x-1\right)$

40.

Divide using synthetic division. $\left(x^4-2x^3+x^2+x-1\right)\div\left(x-1\right)$

a)

$\left(x-1\right)\left(x^3+x^2-1\right)$

b)

$\left(x-1\right)\left(x^3-x^2+1\right)$

c)

$\left(x-1\right)\left(x^3-x^2-1\right)$

d)

$\left(x-1\right)\left(x^3+x^2+x\right)$

Alg 2 - 5.1, 5.3, 5.5 Review (2021-2022)

Total questions: 40

Worksheet time: 10hrs 0mins

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