Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 2

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10th ICSE

IMPORTANT

Earn 100

Using the Remainder Theorem, factorize each of the following completely :

$4 x^{3} + 7 x^{2} - 36 x - 63$

Important Questions on Remainder and Factor Theorems

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 2

Using the Remainder Theorem, factorize each of the following completely :

$x^{3} + x^{2} - 4 x - 4 .$

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 3

Using the Remainder Theorem, factorise the expression

3 x^{3} + 10 x^{2} + x - 6

. Hence, solve the equation

3 x^{3} + 10 x^{2} + x - 6 = 0

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 4

Factorise the expression

f (x) = 2 x^{3} - 7 x^{2} - 3 x + 18

. Hence, find all possible values of x for which

f (x) = 0

.

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 5

Given that

x - 2

and

x + 1

are factors of

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

; calculate the values of

a

and

b

. Hence, find all the factors of

f (x)

.

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 6

The expression

4 x^{3} - b x^{2} + x - c

leaves remainders

0

and

30

when divided by

x + 1

and

2 x - 3

respectively. Calculate the values of

b

and

c

. Hence, factorise the expression completely.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 7

If

x + a

is a common factor of expressions

f (x) = x^{2} + p x + q

and

g (x) = x^{2} + m x + n;

show that:

a = \frac{n - q}{m - p}

.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 8

The polynomials $a x^{3} + 3 x^{2} - 3$ and $2 x^{3} + 5 x + a$ , when divided by $x - 4$ , leave the same remainder in each case. Find the value of $a$ .

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10th ICSE

IMPORTANT

Concise Mathematics>Chapter 8 - Remainder and Factor Theorems>EXERCISE>Q 9

Find the value of

' a'

, if

(x - a)

is a factor of

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

.