Exercises for Question Type 1: Finding factors of a polynomial using factor theorem

Question 1

Skill question

Factorize the polynomial $x^{3} - 10 x^{2} + 31 x - 30$ completely using the factor theorem.

[6]

Question 2

Skill question

Factorize the polynomial $x^{3} - 4 x^{2} - x + 4$ completely using the factor theorem.

[5]

Question 3

Skill question

Factorize the polynomial $x^{3} - 6 x^{2} + 11 x - 6$ completely using the factor theorem.

[6]

Question 4

Skill question

Factorize the polynomial $2 x^{3} - 3 x^{2} - 8 x + 12$ completely using the factor theorem.

[5]

Question 5

Skill question

Factorize the polynomial $x^{3} + x^{2} - 4 x - 4$ completely using the factor theorem.

[5]

Question 6

Skill question

Factorise the polynomial $x^{4} - 16$ completely.

[3]

Question 7

Skill question

Factorize the polynomial $3 x^{3} + 6 x^{2} - 3 x - 6$ completely using the factor theorem.

[7]

Question 8

Skill question

Factorize the polynomial $x^{3} + 2 x^{2} - x - 2$ completely using the factor theorem.

[5]

Question 9

Skill question

Factorize the polynomial $x^{3} - x^{2} - x + 1$ completely using the factor theorem.

[5]

Question 10

Skill question

Factorize the polynomial $x^{4} + x^{3} - x^{2} - x$ completely using the factor theorem. [5 marks]

[5]

Question 11

Skill question

Factorize the polynomial $x^{3} - 2 x^{2} - 5 x + 6$ completely using the factor theorem.

[6]

Question 12

Skill question

Factorize the polynomial $x^{4} - x^{3} - 7 x^{2} + x + 6$ completely using the factor theorem.

[6]

IB Mathematics Analysis and Approaches Question Type 1: Finding Factors of a Polynomial Using Factor Theorem Exercises