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

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The polynomial $x^{3} - 5 x^{2} + 7 x - 3$ , is denoted by $p (x)$ . Find the quotient and remainder when $p (x)$ is divided by $(x^{2} - 2 x - 1)$ .

Important Questions on Algebra

MEDIUM

AS and A Level

IMPORTANT

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

The polynomial

x^{3} - 5 x^{2} + 7 x - 3

, is denoted by

p (x)

. Use the factor theorem to show that

x - 3

is a factor of

p (x)

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 9

The polynomial

4 x^{4} + 4 x^{3} - 7 x^{2} - 4 x + 8

, is denoted by

p (x)

. Find the quotient and remainder when

p (x)

is divided by

(x^{2} - 1)

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 9

The polynomial

4 x^{4} + 4 x^{3} - 7 x^{2} - 4 x + 8

, is denoted by

p (x)

. Find the quotient and remainder when

p (x)

is divided by

(x^{2} - 1)

. Hence solve the equation

4 x^{4} + 4 x^{3} - 7 x^{2} - 4 x + 3 = 0

.

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 10

The polynomial

x^{4} - 48 x^{2} - 21 x - 2

, is denoted by

p (x)

. Find the value of the constant

k

for which

f (x) = (x^{2} + k x + 2) (x^{2} - k x - 1)

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 10

The polynomial

x^{4} - 48 x^{2} - 21 x - 2

, is denoted by

p (x)

. Find the value of constant

k

for which

f (x) = (x^{2} + k x + 2) (x^{2} - k x - 1)

. Hence solve

f (x) = 0

. Give your answers in exact form.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 11

The polynomial

2 x^{4} + 3 x^{3} - 12 x^{2} - 7 x + a

, where

a

is a constant, is denoted by

p (x)

. It is given that

2 x - 1

is a factor of

p (x)

. Find the value of

a

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 11

The polynomial

2 x^{4} + 3 x^{3} - 12 x^{2} - 7 x + a

, where

a

is a constant, is denoted by

p (x)

. It is given that

2 x - 1

is a factor of

p (x)

and also, verify that

x + 3

is a factor of

p (x)

and hence factorise

p (x)

completely.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 12

The polynomial

3 x^{3} + a x^{2} - 36 x + 20

, where

a

is a constant, is denoted by

p (x)

. It is given that

x - 2

is a factor of

p (x)

. Find the value of

a

.