Sample QuestionsRemainder and Factor Theorems questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find , in given case the remainder when:
$x^4+1$ is divided by $x+1$
View full solution →Find the value of ‘m’, if $mx^3 + 2x^2 – 3$ and $x^2 – mx + 4$ leave the same remainder when each is divided by $x – 2$
View full solution →What should be subtracted from $3x^3 – 8x^2 + 4x – 3$, so that the resulting expression has $x + 2$ as a factor?
View full solution →Using remainder theorem, find the value of k if on dividing $2x^3 + 3x^2 - kx + 5$ by $x - 2,$ leaves a remainder $7$
View full solution →When divided by $x-3$ the polynomials $x^3-p x^2+x+6$ and $2 x^3-x^2-(p+3) x-6$ leave the same remainder. Find the value of 'p'.
View full solution →Find the number which should be added to $x^2 + x + 3$ so that the resulting polynomial is completely divisible by $(x + 3).$
View full solution →if $x – 2$ is a factor of $x^2 + ax + b$ and $a + b = 1,$ find the values of $a$ and $b.$
View full solution →When $x^3 + 3x^2 – mx + 4$ is divided by $x – 2,$ the remainder is $m + 3.$ Find the value of $m.$
View full solution →Show that $(x – 1)$ is a factor of $x^3 – 7x^2 + 14x – 8$. Hence, completely factorise the given expression.
View full solution →What must be subtracted from $16x^3 – 8x^2 + 4x + 7$ so that the resulting expression has
$2x + 1$ as a factor?
View full solution →The polynomials $ax^3 + 3x^2 – 3$ and $2x^3 – 5x + a$, when divided by $x – 4$, leave the same remainder in each case. Find the value of a.
View full solution →If $(x + 1)$ and $(x – 2)$ are factors of $x^3 + (a + 1)x^2 – (b – 2)x – 6$, find the values of a and b. And then, factorise the given expression completely.
View full solution →$(3x + 5)$ is a factor of the polynomial $(a – 1)x^3 + (a + 1)x^2 – (2a + 1)x – 15$. Find the value of ‘a’, factorise the given polynomial completely.
View full solution →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.
View full solution →Using the Remainder Theorem, factorise each of the following completely.$3x^3+ 2x^2 − 19x + 6$
View full solution →The expression $2x^3 + ax^2 + bx – 2$ leaves remainder $7$ and $0$ when divided by $2x – 3$ and $x + 2$ respectively. Calculate the values of $a$ and $b$
View full solution →The polynomial $px^3 + 4x^2 – 3x + q$ is completely divisible by $x^2 – 1$; find the values of $p$ and $q$. Also, for these values of p and q factorize the given polynomial completely.
View full solution →Factorise $x^3 + 6x^2 + 11x + 6$ completely using factor theorem.
View full solution →Using Remainder Theorem, factorise:
$x^3 + 10x^2 – 37x + 26$ completely
View full solution →When the polynomial $x^3+2 x^2-5 a x-7$ is divided by $(x-1)$, the remainder is $A$ and when the polynomial $x^3+a x^2-$ $12 x+16$ is divided by $(x+2)$, the remainder is $B$. Find the value of ' $a$ ' if $2 A+B=0$.
View full solution →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 : $a=\frac{n-q}{m-p}$
View full solution →