Sample QuestionsFactorization questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the remainder (without division) when $2x^3 – 3x^2 + 7x – 8$ is divided by $x – 1 (2000)$
View full solution →Using remainder theorem, find the remainder on dividing $f(x)$ by $(x + 3)$ where $f(x) = 3x^3 + 7x^2 – 5x + 1$
View full solution →Using remainder theorem, find the remainder on dividing $f(x)$ by $(x + 3)$ where $f(x) = 2x^2 – 5x + 1$
View full solution →Find the remainder (without divisions) on dividing $f(x)$ by $x – 2$, where $f(x) = 2x^3 – 7x^2 + 3$
View full solution →Find the remainder (without divisions) on dividing $f(x)$ by $x – 2,$ where $f(x) = 5x^2 – 1x + 4$
View full solution →What number must be added to $2x^3 – 7x^2 + 2x$ so that the resulting polynomial leaves the remainder – 2 when divided by $2x – 3?$
View full solution →What number must be subtracted from $2 x^2-5 x$ so that the resulting polynomial leaves the remainder $2$ , when divided by $2 x+1 ?$
View full solution →Using remainder theorem, find the value of a if the division of $x^3 + 5x^2 – ax + 6 by (x – 1)$ leaves the remainder 2a.
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 →Find the remainder (without division) on dividing $3x^2 + 5x – 9 by (3x + 2)$
View full solution →By factor theorem, show that $(x + 3)$ and $(2x – 1)$ are factors of $2x^2 + 5x – 3.$
View full solution →Find ‘a’ if the two polynomials $ax^3 + 3x^2 – 9 $ and $2x^3 + 4x + a$, leaves the same remainder when divided by $x + 3.$
View full solution →QUESIION When divided by $x-3$ the polynomials $x^2-p x^2+x+6$ and $2 x^3-x^2-(p+3) x-6$ leave the same remainder. Find the value of ' $p$ '
View full solution → $(x-2)$ is a factor of the expression $x^3+a x^2+b x+6$. When this expression is divided by $(x-3)$, it leaves the remainder 3 . Find the values of $a$ and $b$.
View full solution →Find the value of the constants $a$ and $b$, if $(x-2)$ and $(x+3)$ are both factors of the expression $x^3+a x^2+b x-12$.
View full solution →Given $f(x)=a x^2+b x+2$ and $g(x)=b x^2+a x+1$. If $x-2$ is a factor of $f(x)$ but leaves the remainder -15 when it divides $g(x)$, find the values of $a$ and $b$. With these values of $a$ and $b$, factorise the expression. $f(x)+g(x)+4 x^2+7 x$.
View full solution →If $ax^3 + 3x^2 + bx – 3$ has a factor $(2x + 3)$ and leaves remainder $– 3$ when divided by $(x + 2)$, find the values of a and b. With these values of a and b, factorise the given expression.
View full solution →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 →If $(x + 2)$ and $(x – 3)$ are factors of $x^3 + ax + b$, find the values of a and b. With these values of a and b, factorise the given expression.
View full solution →f $2 x^3+a x^2-11 x+b$ leaves remainder $0$ and $42 $when divided by $(x-2)$ and $(x-3)$ respectively, find the values of a and $b$. With these values of $a$ and $b$, factorize the given expression.
View full solution →Given$ f(x) = ax^2 + bx + 2$ and $g(x) = bx^2 + ax + 1. If x – 2$ is a factor of $f(x)$ but leaves the remainder $– 15$ when it divides $g(x),$ find the values of $a$ and $b.$ With these values of $a$ and $b,$ factorise the expression.$ f(x) + g(x) + 4x^2 + 7x.$
View full solution →If $ax^3 + 3x^2 + bx – 3$ has a factor $(2x + 3)$ and leaves remainder $– 3$ when divided by $(x + 2),$ find the values of a and $b.$ With these values of $a$ and $b,$ factorise the given expression.
View full solution →$If\ (x – 2)$ is a factor of the expression $2x^3 + ax^2 + bx – 14$ and when the expression is divided by $(x – 3),$ it leaves a remainder $52,$ find the values of $a$ and $b.$
View full solution →$If\ (x + 2)$ and $(x – 3)$ are factors of $x^3 + ax + b,$ find the values of $a$ and $b$. With these values of $a$ and $b,$ factorise the given expression.
View full solution →$f\ 2x^3 + ax^2 – 11x + b$ leaves remainder $0$ and $42$ when divided by $(x – 2)$ and $(x – 3)$ respectively, find the values of $a$ and $b$. With these values of $a$ and $b,$ factorize the given expression.
View full solution →If $x+1$ is a factor of $3 x^3+k x^2+7 x+4$, then the value of $k$ is
Answer: C.
View full solution →If on dividing $2 x^3+6 x^2-(2 k-7) x+5$ by $x+3$, the remainder is $k-1$ then the value of $k$ is
Answer: D.
View full solution →If on dividing $4 x^2-3 k x+5$ by $x+2$, the remainder is -3 then the value of $k$ is
Answer: B.
View full solution →When $2 x^3-x^2-3 x+5$ is divided by $2 x+1$, then the remainder is
Answer: A.
View full solution →When $x^3-3 x^2+5 x-7$ is divided by $x-2$, then the remainder is
Answer: D.
View full solution →