Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 2

EASY

AS and A Level

IMPORTANT

Earn 100

Use the factor theorem to show that $(2 x - 5)$ is a factor of $(2 x^{3} - 7 x^{2} + 9 x - 10)$ .

Important Questions on Algebra

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 3

Given that

(x + 4)

is a factor of

(x^{3} + a x^{2} - 29 x + 12)

, find the value of

- a

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 4

Given that

(x - 3)

is a factor of

(x^{3} + a x^{2} + b x - 30)

, express

a

in terms of

b

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 5

Given that

(2 x^{2} + x - 1)

is a factor of

(2 x^{3} - x^{2} + a x + b)

, find the value of

a

and the value of

b

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 6

Given that

(x - 3)

and

(2 x + 1)

are factors of

(2 x^{3} + p x^{2} + (2 q - 1) x + q)

. Find the value of

p

and the value of

q

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 6

Given that $(x - 3)$ and $(2 x + 1)$ are factors of $(2 x^{3} + p x^{2} + (2 q - 1) x + q)$ .

Explain why

(x + 2)

is also a factor of the expression.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 7

It is given that

(x + a)

is a factor of

(x^{3} + 4 x^{2} + 7 a x + 4 a)

. Find the possible values of

a

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 8

It is given that

(x + 1)

is a common factor of

(x^{3} + p x + q)

and

(x^{3} + (1 - p) x^{2} + 19 x - 2 q)

. Find the value of

p

and the value of

q

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>EXERCISE 1E>Q 8

It is given that $(x + 1)$ is a common factor of $(x^{3} + p x + q)$ and $(x^{3} + (1 - p) x^{2} + 19 x - 2 q)$ .

When

p

and

q

have some values, factorise

x^{3} + p x + q

and

x^{3} + (1 - p) x^{2} + 19 x - 2 q

completely.