Free Printable Proving Polynomial Identities

1.

Which answer properly places the polynomial in the correct descending order?

$6x^2+7x^4+5x^3+15-8x$

a)

$7x^4-8x+6x^2-5x^3+15$

b)

$5x^3+7x^4-8x+6x^2+15$

c)

$15-8x+7x^4+6x^2+5x^3$

d)

$7x^4+5x^3+6x^2-8x+15$

2.

Which answer properly places the polynomial in the correct descending order?

$9x^5-3x^2+8x-18$

a)

$9x^5-3x^2+8x-18$

b)

$-3x^2+8x-18+9x^5$

c)

$-18+9x^5-3x^2+8x$

d)

$-18+9x^5+8x-3x^2$

3.

What is the degree of the polynomial

$7x^4-8x^6+2x^2-10$

a)

4

b)

6

c)

2

d)

0

4.

What is the degree of the polynomial

$10x^3-7x^2+9x^5-x^8+7$

a)

3

b)

2

c)

5

d)

8

5.

What is the name of the polynomial shown?

$7x^3+5x^2-8x+10$

a)

Cubic

b)

Quartic

c)

Quadratic

d)

Zero

6.

What is the name of the polynomial shown?

$-3x^5+8x^2-10+7x-4x^3$

a)

Cubic

b)

7th degree Polynomial

c)

Quintic

d)

Zero

7.

Name the following polynomial

$5x^2+2x-10$

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with degree of 0

8.

Name the following polynomial

$-3x^4+6x$

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with degree of 0

9.

Name the following polynomial

$7x^3y^2$

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with degree of 0

10.

Name the polynomial and the number of terms

$8x^2+6x-16$

a)

Trinomial with 3 terms

b)

Binomial with 2 terms

c)

Polynomial with 4 terms

d)

Monomial with 2 terms

11.

Name the polynomial and the number of terms

$-12x^4$

a)

Trinomial with 3 terms

b)

Binomial with 2 terms

c)

Polynomial with 4 terms

d)

Monomial with 1 term

12.

Name the polynomial by degrees and number of terms

$5x^4+8x^2-10x$

a)

Polynomial, 4 degrees, 3 terms

b)

Binomial, 4 degrees, 2 terms

c)

Monomial, 4 degrees, 1 term

d)

Trinomial, 4 degrees, 3 terms

13.

Name the polynomial by degrees and number of terms

$10x^3+7x^2$

a)

Polynomial, 3 degrees, 2 terms

b)

Binomial, 4 degrees, 2 terms

c)

Trinomial, 4 degrees, 2 terms

d)

Monomial, 4 degrees, 1 term

14.

Write the following polynomial in descending order in terms of b

$b^3-a^2b+4ab^4-10a$

a)

$4ab^4+b^3-a^2b-10a$

b)

$-10a+4ab^4-a^2b+b^3$

c)

$-a^2b-10a+4ab^4+b^3$

15.

$x^{2\ }-y^{2\ }=$

a)

$\left(x+y\right)^2\ -2xy$

b)

(x+y)(x-y)

c)

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

d)

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

16.

(x+y) ² =

a)

x²+y²-2xy

b)

x^2-y²-2xy

c)

x^2-y²-2xy

d)

x²+y²+2xy

17.

(x-y) ² =

a)

x²+y²-2xy

b)

x^2-y²-2xy

c)

x^2-y²-2xy

d)

x²+y²+2xy

18.

x²+y²-2xy

a)

(x-y)²

b)

x^2-y²

c)

(x+y)²

d)

x²+y²

19.

x²+y²+2xy

a)

(x-y)²

b)

x^2-y²

c)

(x+y)²

d)

x²+y²

20.

(x-y)(x+y)

a)

(x-y)²

b)

x^2-y²

c)

(x+y)²

d)

x²+y²

21.

(x+a)(x+b)

a)

x²+a²+b²

b)

x²+(a-b)x + ab

c)

x²+(a+b)x +ab

d)

x²+(a+b)x +2ab

22.

x²+(a+b)x +ab

a)

(x-a)(x-b)

b)

(x-a)(x+b)

c)

(x+a)(x+b)

d)

(x+a)(x-b)

23.

(x-y)(x²+xy +y²⁾

a)

x³-y³

b)

x³⁺y³

c)

x²-y²

d)

x²⁺y²

24.

(x+y)(x²-xy +y²⁾

a)

x³-y³

b)

x³⁺y³

c)

x²-y²

d)

x²⁺y²

25.

x³-y³

a)

(x+y)(x²+xy +y²)

b)

(x-y)(x²+xy +y²)

c)

(x+y)(x²-xy +y²⁾

d)

(x-y)(x²-xy +y²⁾

26.

x³+y³

a)

(x+y)(x²+xy +y²)

b)

(x-y)(x²+xy +y²)

c)

(x+y)(x²-xy +y²⁾

d)

(x-y)(x²-xy +y²⁾

27.

(x+y)³

a)

x³+y³-3xy(x+y)

b)

x³+y³+3xy(x+y)

c)

x³+y³-3xy(x-y)

d)

x³+y³+3xy(x-y)

28.

(x-y)³

a)

x³-y³-3xy(x-y)

b)

x³-y³+3xy(x-y)

c)

x³+y³-3xy(x-y)

d)

x³-y³+3xy(x+y)

29.

x³-y³-3xy(x-y)

a)

(x+y)³

b)

(x-y)³

c)

(x-y)²+(x+y)²

d)

x³-y³

30.

x³+y³+z³-3xyz

a)

(x+y+z)(x²+y²+z²+xy +yz+xz)

b)

(x-y-z)³

c)

(x+y+z)(x²+y²+z²-xy -yz-xz)

d)

(x+y+z)³

31.

(x+y+z)(x²+y²+z²-xy -yz-xz)

a)

x³+y³+z³-3xyz

b)

(x-y-z)³

c)

x³+y³+z³+3xyz

d)

(x+y+z)³

32.

(x+y)³

a)

x³+y³-3x²yx -3xy²

b)

x³+y³+3x²yx +3xy²

c)

x³+y³+3x²yx -3xy²

d)

x³+y³-3x²yx +3xy²

33.

Identify the following polynomial. $u^2+10uv+25v^2$

a)

Difference of Squares

b)

Square of a Sum

c)

Sum of Cubes

d)

Difference of Cubes

34.

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

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

35.

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

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

36.

Identify the following polynomial.
$250x^4+128x$

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

37.

$x^{2\ }-y^{2\ }=$

a)

$\left(x+y\right)^2\ -2xy$

b)

(x+y)(x-y)

c)

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

d)

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

38.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

39.

Factor $4x^{2\ }-\ 12x\ +\ 9$ completely

a)

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

b)

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

c)

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

d)

Cannot be SOLVED

40.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

(3x - 7y³)(3x + 21xy +7y³)

41.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

42.

Put into standard form: (x + 6)²

a)

x² + 6x + 12

b)

x² + 6x + 36

c)

x² + 36

d)

x² + 12x + 36

43.

Put into standard form: (x - 9)²

a)

x² + 81

b)

x² - 18x + 81

c)

x² + 18x + 81

d)

x² - 81

44.

Find the product:
(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

45.

Identify the following polynomial. $u^2+10uv+25v^2$

a)

Difference of Squares

b)

Square of a Sum

c)

Sum of Cubes

d)

Difference of Cubes

46.

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

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

47.

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

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

48.

Identify the following polynomial.
$250x^4+128x$

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

49.

$x^{2\ }-y^{2\ }=$

a)

$\left(x+y\right)^2\ -2xy$

b)

(x+y)(x-y)

c)

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

d)

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

50.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

51.

Factor $4x^{2\ }-\ 12x\ +\ 9$ completely

a)

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

b)

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

c)

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

d)

Cannot be SOLVED

52.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

(3x - 7y³)(3x + 21xy +7y³)

53.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

54.

Put into standard form: (x + 6)²

a)

x² + 6x + 12

b)

x² + 6x + 36

c)

x² + 36

d)

x² + 12x + 36

55.

Put into standard form: (x - 9)²

a)

x² + 81

b)

x² - 18x + 81

c)

x² + 18x + 81

d)

x² - 81

56.

Find the product:
(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

Proving Polynomial Identities

Total questions: 56

Worksheet time: 1hrs 24mins

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