Free Printable Algebra 1 Polynomials Test Review

1.

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

2.

Multiply:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

3.

(2x - 7)(2x + 7)

a)

2x² + 7x - 49

b)

4x² - 7x + 49

c)

4x² - 49

d)

2x² + 49

4.

Simplify
(p − 8)²
Hint: (p − 8)² = (p − 8)(p − 8)

a)

p ² − 16p − 64

b)

p ² + 16p + 64

c)

p ² − 16p − 8

d)

p ² − 16p + 64

5.

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

6.

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

7.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

8.

What is the degree of the polynomial: 7x³y – 8x² + 9x

a)

6

b)

4

c)

7

d)

3

9.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

10.

Simplify the following expression:

-8(5b + 2) - 7(b - 5)

a)

-33b + 19

b)

-47b² + 21

c)

33b - 19

d)

-47b +19

11.

What is the leading coefficient of the following polynomial?

4x³-2y²x²- 5x⁷y⁷+ 7x⁸

a)

4

b)

7

c)

5

d)

-5

12.

$\frac{\left(-18x^5-12x^3-6x^2\right)}{-3x}$

a)

$-15x^4-9x^2-3x$

b)

$-6x^4-4x^2-2x$

c)

$6x^4+4x^2+2x$

d)

$6x^5+4x^3+2x^2$

13.

Factor:
x² - 10x - 24

a)

(x + 12)(x - 2)

b)

(x - 6)(x - 4)

c)

(x - 12)(x + 2)

d)

(x +6)(x - 4)

14.

Classify:
2n³

a)

Cubic Monomial

b)

cubic Binomial

c)

cubic Trinomial

d)

Polynomial

15.

Classify:
2x⁴+14x³−2x²

a)

quadratic Monomial

b)

quartic Binomial

c)

quartic Trinomial

d)

quadratic Polynomial

16.

Classify by the DEGREE:
2x² - 5

a)

1

b)

2

c)

3

d)

4

17.

What is the highest degree among terms in this polynomial?

6x² + 7x⁴ + x3 + x

a)

1

b)

2

c)

3

d)

4

18.

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

19.

What is the area?

a)

$2x^2-9x-18$ square inches

b)

$2x^2-18$ square inches

c)

$6x-3$ square inches

20.

Which of these is in standard form?

(more than 1 answer)

a)

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

b)

$5-3x$

c)

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

d)

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

e)

$x-2x^2$

21.

Factor the polynomial.
x²-4x-32

a)

(x-8)(x+4)

b)

(x-4)(x-32)

c)

(x+3)(x-4)

d)

(x+2)(x+5)

22.

Factor:
2m² + 3m - 9

a)

2(m + 3)(m - 3)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

23.

What is the first step when factoring polynomials?

a)

Find the GCF

b)

List all the terms

c)

Make a triangle

d)

Write the answer

24.

What is the GCF?

5x + 25

a)

x

b)

5

c)

-5

d)

-x

25.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

26.

This is written in standard form.

6x² + 7x⁴ + x

a)

true

b)

false

27.

Divide:
(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

28.

Simplify by combining like terms:
5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

29.

5x + 3y + 5 + 4x + 3y + y + 8

a)

9x + 7y + 13

b)

6x + 2y + 2

c)

25x + 2y + 3

d)

x + 7y + 12

30.

Classify by number of terms:
3x² – 8x + 1

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

31.

Multiply

(4x+3)(2x-1)

a)

8x²- 2x - 3

b)

8x - 3

c)

8x²+ 6x - 3

d)

8x²+ 2x - 3

Algebra 1 Polynomials Test Review

Total questions: 31

Worksheet time: 1hrs 8mins

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