Remainder Theorem and Factor Theoerem - ICSE STD 10 Mathematics Questions

Find the value of $p$ if $x^3+p x+2 p-2$ is exactly divisible by $(x+1)$.

If $p(x)=2 x^3+3 x^2-a x-b$ is divided by $(x-1)$, the remainder is 6 , then find the value of $a+b$.

Find $a$, if the two polynomials $a x^3+3 x^2-9$ and $2 x^3+4 x+a$ leave the same remainder when divided by $(x+3)$. Also, find the remainder.

View full solution →

Q 4[3 marks sum]3 Marks

Find the value of $k$, if $(x-2)$ is a factor of $x^3+2 x^2-k x+10$. Hence, determine whether $(x+5)$ is also a factor.

View full solution →

Q 5[3 marks sum]3 Marks

When divided by $(x-3)$, the polynomials $p(x)=x^3-p x^2+x+6$ and $q(x)=2 x^3-x^2-(p+3) x-6$ leave the same remainder. Find the value of $p$. Also, find the remainder.

View full solution →

Q 6[4 marks sum]4 Marks

Using the remainder theorem and factor theorem, factorise the following polynomial : $x^3+10 x^2-37 x+26$.

View full solution →

Q 7[4 marks sum]4 Marks

If $(x-2)$ is a factor of the expression, $2 x^3+a x^2+b x-14$ and when the expression is divided by $(x-3)$, it leaves a remainder 52 , find the values of $a$ and $b$.

View full solution →

Q 8[4 marks sum]4 Marks

Using the remainder theorem, factorise completely the following polynomial: $3 x^3+2 x^2-19 x+6$

View full solution →

Q 9[4 marks sum]4 Marks

Given that $(x+2)$ and $(x+3)$ are factors of $2 x^3+a x^2+7 x-b$, Determine the values of $a$ and $b$.

View full solution →

Q 10[4 marks sum]4 Marks

If $(x-2)$ is a factor of $2 x^3-x^2-p x-2$,
(a) find the value of $p$.
(b) with the value of $p$, factorise the above expression completely.

View full solution →

Q 11MCQ1 Mark

On dividing $x^2-4 x+m$ by $(x-2)$, the remainder is -1 . The value of $m$ is :

A
1
B
2
C
-2
D
3

View full solution →

Q 12MCQ1 Mark

Given $f(x)=(3 k+2) x^3+(k-1)$. If $f(x)$ is divided by $(2 x+1)$, the remainder is :

A
$f\left(\frac{1}{2}\right)$
B
$f\left(-\frac{1}{2}\right)$
C
$f(2)$
D
$f(-2)$

View full solution →

Q 13MCQ1 Mark

$(x+2)$ and $(x+3)$ are factors of $f(x)=x^3+a x+b$, then the value of $f(-3)$ is :

A
$1$
B
$2$
C
$-1$
D
$0$

View full solution →

Q 14MCQ1 Mark

If $(x-3)$ is a factor of $f(x)=x^2-k x+12$, then the other factor of $f(x)$ is :

A
$x-4$
B
$x-1$
C
$x-2$
D
$x+4$

View full solution →

Q 15MCQ1 Mark

Given $f(x)=x^3+(k x+8) x+k$. If $f(x)$ is divided by $(x+1)$, the remainder is :

A
$2 k-9$
B
$2 k+9$
C
$2 k$
D
$0$

View full solution →

Q 16Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : If $(y-2)$ is a factor of $p(y)=y^3-m x-12$, then the value of $m$ is -1 .
Reason (R) : If $(x+a)$ is a factor of $p(x)$, then $p(-a)=0$.

View full solution →

Q 17Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : $(x+1)$ is a factor of the polynomial $p(x)=x^3+2 x^2-x-2$
Reason (R) : If $(x-a)$ is a factor of $p(x)$, then $p(a)=0$.

View full solution →

Q 18Assertion (A) & Reason (B) MCQ1 Mark

Assertion (A) : When $p(x)=x^4+2 x^3-3 x^2+x-1$ is divided by $(x-2)$, the remainder is $21.$
Reason (R) : If $(x+a)$ is a factor of $p(x)$, then $p(a)=0$.

View full solution →

Remainder Theorem and Factor Theoerem question types

Remainder Theorem and Factor Theoerem questions

Generate a Remainder Theorem and Factor Theoerem paper free

Remainder Theorem and Factor Theoerem Mathematics - Remainder Theorem and Factor Theoerem

Remainder Theorem and Factor Theoerem question types

Remainder Theorem and Factor Theoerem questions

Generate a Remainder Theorem and Factor Theoerem paper free