Free Printable Algebra, Units 5, 6 Review

1.

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

2.

Simplify (2x + 5y - z) + (-6x - 4y + 7z)

a)

-4x +6y + 6z

b)

4x + y + 6z

c)

-4x - y + 6z

d)

-4x + y + 6z

3.

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

4.

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

5.

(x+3)(x+1)

a)

x²+3x+3

b)

2x+4x+3

c)

x²+4x+3

d)

5x + 3

6.

5x(2x + 3)

a)

10x²+ 15x

b)

7x + 15x

c)

7x² + 8x

d)

25x²

7.

Use memory of special cases: ( g + 4) ( g - 4)

a)

g² - 16

b)

2g - 16

c)

g² - 16x -16

d)

g² - 4x - 8

8.

Simplify.

a)

x - 3xy + 2

b)

x + 3xy + 2

c)

x - 3xy - 2

d)

-x - 3xy - 2

9.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

10.

Factor:
56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

11.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁶)

d)

3x²(80x³-40-60x⁵)

12.

Factor:
2n³+16n+12

a)

2n(n³+24n+6)

b)

2(n³+8n+6)

c)

2n(n³+8n+6)

d)

3(n³+8n+6)

13.

Factor
x² + 4x + 3

a)

(x - 1)(x - 3)

b)

(x + 1)(x + 3)

c)

(x - 1)(x + 3)

d)

(x + 1)(x - 3)

14.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

15.

Factor:
x² - 6x + 9

a)

(x - 3)(x + 3)

b)

(x - 3) (x - 3)

c)

(x + 3) (x + 3)

d)

Prime polynomial

16.

x²-4

a)

(x+2)(x-2)

b)

(x+1)(x-4)

c)

(x-2)(x-2)

d)

(x+4)(x-1)

17.

Factor:
2m² + 3m - 9

a)

2(m + 3)(m - 3)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

18.

Factor
2x² - 13x - 70

a)

(2x-7)(x+10)

b)

(7x+5)(x+2)

c)

(2x+7)(x-10)

d)

2(x+7)(x+10)

19.

Factor by grouping:
$x^3-4x^2-4x+16$

a)

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

b)

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

c)

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

d)

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

20.

Factor by grouping:

4p^3+8p^2+3p+6

a)

$\left(2p^2+3\right)\left(p+2\right)$

b)

$\left(2p^2+6\right)\left(p+4\right)$

c)

$\left(4p^2+3\right)\left(p+2\right)$

d)

$\left(4p^2+8p\right)\left(3p+6\right)$

21.

Factor the following expression:
$2x^2+12x-54$

a)

$\left(x-6\right)\left(x-10\right)$

b)

$2\left(x-9\right)\left(x+3\right)$

c)

$2\left(x+9\right)\left(x-3\right)$

d)

Not Factorable (prime)

22.

Factor the following expression:
$2m^2-18$

a)

$2\left(m+3\right)\left(m-3\right)$

b)

$2\left(m-3\right)^2$

c)

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

d)

$2\left(5m+2\right)\left(5m-2\right)$

23.

Factor Completely.

4x^3-x^2-4x+1

a)

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

b)

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

c)

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

d)

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

24.

Factor the following expression:
$4n^2+20n-24$

a)

$4\left(n-1\right)\left(n+6\right)$

b)

$4\left(n-1\right)\left(n-6\right)$

c)

$n\left(n-9\right)$

d)

$\left(n+3\right)\left(n-3\right)$

25.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

Algebra, Units 5, 6 Review

Total questions: 25

Worksheet time: 1hrs 15mins

Similar Resources on Wayground