Polynomials: Master Expanding and Factoring for Year 11 Maths

Question 1

Solve the equation: x^3 - 8 = 0

Accepted Answer

x = 2 or x = -2

Answer

x = 2

Answer

x = -2

Answer

x = 2 or x = -2 or x = 0

Question 2

Which of the following is a cubic expression?

Accepted Answer

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

Answer

x^2 + 2x + 1

Answer

2x^2 - 5x + 3

Answer

x^2 - 4

Question 3

Factor the polynomial expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 3)^2

Answer

(x - 3)^2

Answer

(x - 9)(x + 9)

Question 4

Find the degree of the polynomial: 3x^4 - 2x^2 + 5

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 5

Factorise the polynomial x^3 - 8.

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x + 2)(x^2 - 2x - 4)

Answer

x(x - 2)(x + 4)

Question 6

Factorise the following expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)(x - 2)

Answer

(x + 2)(x + 2)

Answer

(x - 4)(x + 1)

Question 7

Complete the square for the expression x^2 + 6x + __

Accepted Answer

9

Answer

3

Answer

12

Answer

18

Question 8

Factorise the following cubic expression: x^3 - 8

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 2)(x^2 - 2x - 4)

Answer

(x + 2)(x^2 + 2x - 4)

Question 9

Simplify the following expression: (x - 2)(x + 2) - (x - 3)(x + 3)

Accepted Answer

8

Answer

-8

Answer

4

Answer

-4

Question 10

Which of the following is a factor of x^4 - 16?

Accepted Answer

x^2 - 4

Answer

x - 2

Answer

x + 2

Answer

x^2 + 4

Question 11

Complete the square for the expression x^2 + 6x.

Accepted Answer

x^2 + 6x + 9

Answer

x^2 + 6x + 18

Answer

x^2 + 6x + 3

Answer

x^2 + 6x + 12

Question 12

Solve the polynomial inequality x^2 - 5x + 6 > 0.

Accepted Answer

x < 2 or x > 3

Answer

x > 2 or x < 3

Answer

x < 2 and x > 3

Answer

x > 2 and x < 3

Question 13

Factorise: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)(x - 3)

Answer

(x - 9)

Answer

(x + 9)

Question 14

Complete the square to rewrite x² + 6x as a perfect square trinomial:

Accepted Answer

x² + 6x + 9

Answer

x² + 6x - 9

Answer

x² - 6x + 9

Answer

x² - 6x - 9

Question 15

Factorise: x³ + 2x² - 3x

Accepted Answer

x(x - 1)(x + 3)

Answer

x(x + 1)(x - 3)

Answer

(x - 1)(x + 3)

Answer

(x + 1)(x - 3)

Question 16

Which of the following is a quadratic expression?

Accepted Answer

x² + 3x - 4

Answer

x³ - 2

Answer

x + 2

Answer

2x³ - 5

Question 17

Expand and simplify the expression (2x + 3)(x - 5):

Accepted Answer

2x^2 - 10x + 15

Answer

2x^2 - 7x - 15

Answer

2x^2 + 7x - 15

Answer

2x^2 + 10x + 15

Question 18

Simplify the expression (x + 2)^2:

Accepted Answer

x^2 + 4x + 4

Answer

x^2 - 4x + 4

Answer

x^2 + 4

Answer

x^2 - 4

Question 19

Identify the polynomial among the following expressions:

Accepted Answer

x^2 + 2x

Answer

√x + 1

Answer

sin(x)

Answer

e^x

Question 20

Expand and simplify the cubic expression (x - 3)^3:

Accepted Answer

x^3 - 9x^2 + 27x - 27

Answer

x^3 + 9x^2 + 27x + 27

Answer

x^3 - 3x^2 + 9x - 27

Answer

x^3 + 3x^2 + 9x + 27

Question 21

Factorize the polynomial: x^3 - 8

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 8)(x^2 + 8x + 64)

Answer

Cannot be factored

Question 22

Simplify the polynomial: (x^2 - 4)(x^2 + 4)

Accepted Answer

x^4 - 16

Answer

x^4 + 16

Answer

x^2 - 16

Answer

x^2 + 16

Question 23

Which of the following is the correct factorized form of the quadratic expression **x² - 9**?

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)(x + 3)

Answer

(x - 3)²

Answer

(x + 3)²

Question 24

Expand the brackets in the expression **(x + 2)²**:

Accepted Answer

x² + 4x + 4

Answer

x² + 4

Answer

x² + 2x + 4

Answer

x² - 4

Question 25

Which of the following is NOT a technique for simplifying polynomials?

Accepted Answer

Substitution

Answer

Factoring

Answer

Combining like terms

Answer

Rearranging terms

Question 26

Factorise the expression x^2 - 9 as a product of two binomials.

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 9)(x - 1)

Answer

Cannot be factorised

Question 27

Solve the quadratic equation x^2 - 5x + 6 = 0 by factorisation.

Accepted Answer

x = 2 or x = 3

Answer

x = -2 or x = -3

Answer

x = 1 or x = 6

Answer

x = -1 or x = -6

Question 28

Which of the following is a zero of the polynomial x^2 - 4x + 3?

Accepted Answer

x = 2

Answer

x = 1

Answer

x = 3

Answer

x = 4

Question 29

Expand and simplify the expression (x - 2)(x + 3) - (x - 1)^2.

Accepted Answer

x^2 + x - 5

Answer

x^2 - x - 5

Answer

x^2 + 2x - 5

Answer

x^2 - 2x - 5

Question 30

Find the value of k for which the expression x^2 + kx + 9 is a perfect square trinomial.

Accepted Answer

k = 6

Answer

k = -6

Answer

k = 12

Answer

k = -12

Question 31

Factor the expression x^2 - 25 into its simplest form.

Accepted Answer

(x - 5)(x + 5)

Answer

(x - 2)(x + 2)

Answer

(x - 3)(x + 3)

Answer

(x - 4)(x + 4)

Question 32

Identify the difference of two squares from the following options:

Accepted Answer

x^2 - 4

Answer

x^2 + 4

Answer

x^2 + 2x + 1

Answer

x^2 - 2x + 1

Question 33

Simplify the polynomial expression (2x^2 - 5x + 3) - (x^2 - 2x + 1).

Accepted Answer

x^2 - 7x + 2

Answer

x^2 + 7x - 2

Answer

x^2 - 3x + 4

Answer

x^2 + 3x - 4

Question 34

Find a factor of the polynomial x^2 + 5x + 6.

Accepted Answer

(x + 3)

Answer

(x + 2)

Answer

(x - 3)

Answer

(x - 2)

Question 35

Solve the polynomial equation 2x(x - 1) = 0.

Accepted Answer

x = 0, 1

Answer

x = 1, 2

Answer

x = 0, 2

Answer

x = -1, 0

Question 36

Identify the polynomial of degree 4:

Accepted Answer

x^4 + 3x^2 - 2

Answer

x^2 + 2x - 3

Answer

x^3 - 5x^2 + 2x

Answer

x^5 - 2x^3 + x

Question 37

Simplify: (2x - 3)(2x + 3) - 4x^2

Accepted Answer

0

Answer

4x

Answer

-4x

Answer

12

Question 38

Which of the following is NOT a standard method for expanding polynomials?

Accepted Answer

Substitution

Answer

FOIL

Answer

Grouping

Question 39

Which of the following is a factor of the quadratic polynomial x^2 + 5x + 6?

Accepted Answer

(x + 2)

Answer

(x - 2)

Answer

(x + 3)

Question 40

Expand the following polynomial using the cube formula: (x - y)^3

Accepted Answer

x^3 - 3x^2y + 3xy^2 - y^3

Answer

x^3 + 3x^2y - 3xy^2 - y^3

Answer

x^3 + 3xy^2 + 3x^2y - y^3

Answer

x^3 - 3xy^2 + 3x^2y - y^3

Question 41

Which of the following polynomials has a degree of 4?

Accepted Answer

x^4 - 2x^3 + 5x^2 - 3x + 7

Answer

x^2 - 2x + 5

Answer

x + 7

Answer

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

Question 42

What is the expanded form of the expression (2x + 3)(x - 5)?

Accepted Answer

2x² - 7x - 15

Answer

2x² + 7x - 15

Answer

2x² - 7x + 15

Answer

2x² + 7x + 15

Question 43

What is the factored form of 4x² + 12x + 9?

Accepted Answer

(2x + 3)²

Answer

(4x - 3)²

Answer

(4x + 3)²

Answer

(2x - 3)²

Question 44

Which of the following is a cubic polynomial?

Accepted Answer

2x³ - 5x + 1

Answer

4x⁴ + 2x² - 1

Answer

5x - 7

Answer

x² - 3x + 2

Question 45

What is the degree of the polynomial 7x⁵ - 3x² + 2?

Accepted Answer

5

Answer

3

Answer

7

Answer

2

Question 46

What is the fully factored form of 2x³ - 16?

Accepted Answer

2(x - 2)(x² + 2x + 4)

Answer

(2x + 4)(x² - 2x + 4)

Answer

2(x + 2)(x² - 2x + 4)

Answer

(2x - 4)(x² + 2x + 4)

Question 47

Which of the following is NOT a polynomial?

Accepted Answer

2x^(-1) + 3x² - 1

Answer

5x³ - 2x + 7

Answer

4x² + 9

Answer

x⁴ - 6x³ + 2x

Question 48

Which of the following expressions represents a polynomial?

Accepted Answer

3x² - 5x + 2

Answer

2√x + 7

Answer

√5x⁻² + 3x

Answer

4 / (x - 1)

Question 49

What is the degree of the polynomial 6x⁴ - 2x³ + 5?

Accepted Answer

4

Answer

3

Answer

1

Answer

5

Question 50

Expand the following expression: (x + 3)(x - 2)

Accepted Answer

x² + x - 6

Answer

x² - x - 6

Answer

x² - 5x - 6

Answer

x² + 5x - 6

Question 51

Factorise completely: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

(x + 3)²

Answer

(x - 3)²

Question 52

Which of the following is a factorization of the expression 4x² + 12x + 9?

Accepted Answer

(2x + 3)²

Answer

(4x + 3)(x + 3)

Answer

(2x + 6)(2x + 1)

Answer

(2x + 9)(2x + 1)

Question 53

Factorise the expression: 27x³ - 8

Accepted Answer

(3x - 2)(9x² + 6x + 4)

Answer

(3x + 2)(9x² - 6x + 4)

Answer

(3x + 2)(9x² + 6x - 4)

Answer

(3x - 2)(9x² - 6x - 4)

Question 54

The area of a rectangle is represented by the polynomial 2x² + 7x - 15. If the width is (x + 5), what is the length?

Accepted Answer

2x - 3

Answer

x + 3

Answer

x - 3

Answer

2x + 3

Question 55

Simplify the expression: (3x² - 5x + 2) - (x² + 2x - 1)

Accepted Answer

2x² - 7x + 3

Answer

4x² - 3x + 1

Answer

4x² - 7x + 3

Answer

2x² - 3x + 1

Question 56

What is the remainder when the polynomial x³ - 2x² + 5x - 3 is divided by (x - 2)?

Accepted Answer

7

Answer

1

Answer

-1

Answer

5

Question 57

A polynomial function is defined as f(x) = x³ + kx² - 4x + 6. If f(-2) = 0, what is the value of k?

Accepted Answer

1

Answer

-1

Answer

-2

Answer

2