Remainder And Factor Theorems - ICSE STD 10 Mathematics Questions

Prove that $(x-3)$ is a factor of $x^3 - x^2 - 9x +9$ and hence factorize it completely.

Find the value of m ·when $x^3 + 3x^2 -m x +4$ is exactly divisible by $(x-2)$

Using remainder theorem, find the value of m if the polynomial $f(x)= x^3 + 5x^2 -mx +6$ leaves a remainder $2\ m$ when divided by $(x-1)$,

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Q 4[2 Mark Question Answer]2 Marks

Prove by factor theorem that
$(x - 3)$ is a factor of $5x^2 - 21 x +18$

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Q 5[2 Mark Question Answer]2 Marks

Prove by factor theorem that
$(x-2)$ is a factor of $2x^3- 7x -2$

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Q 6[2 Mark Question Answer]2 Marks

Prove that $(x - y)$ is a factor of $yz( y^2 - z^2) + zx( z^2 - x^2) + xy ( x^2 - y^2)$

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Q 7[3 marks sum]3 Marks

Find the values of a and b when the polynomials $f(x)= 2x^2 -5x +a$ and $g(x)= 2x^2 + 5x +b$ both have a factor $(2x+1)$.

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Q 8[3 marks sum]3 Marks

Prove by factor theorem that
$(2x - 1)$ is a factor of $6x^3 - x^2 - 5x +2$

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Q 9[3 marks sum]3 Marks

Prove by factor theorem that
$(3x-2)$ is a factor of $18x^3 - 3x^2 + 6x -12$

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Q 10[3 marks sum]3 Marks

Prove by factor theorem that
$(2x+1)$ is a factor of $4x^3 + 12x^2 + 7x +1$

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Q 11[3 marks sum]3 Marks

What number should be added to polynomial $f(x)= 12x^3 + 16x^2 - 5x - 8$ so that the resulting polynomial is exactly divisible by $(2x - 1) ?$

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Q 12[5 marks sum]5 Marks

Find the values of a and b in the polynomial $f(x) = 2x^3 + ax^2 + bx + 10$, if it is exactly divisible by $(x+2)$ and $(2x-1).$

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Q 13[5 marks sum]5 Marks

The polynomial $f(x) = ax^4 + x^3 + bx^2 - 4x + c$ has $(x + 1), (x-2)$ and $(2x - 1)$ as its factors. Find the values of $a,b,c,$ and remaining factor.

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Q 14[5 marks sum]5 Marks

use the rernainder theorem to find the factors of $( a-b )^3 + (b-c )^3 + ( c-a)^3$

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Q 15[5 marks sum]5 Marks

Find the values of a and b when the factors of the polynomial $f(x)= ax^3 + bx^2 + x a$ are $(x+3)$ and $(2x-1).$ Factorize the polynomial completely.

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Q 16[4 marks sum]4 Marks

Find the values of $m$ and $n$ when the polynomial $f(x)=x^3-2 x^2+m x+n$ has a factor $(x+2)$ and leaves a remainder 9 when divided by $( x +1$ ).

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Q 17[4 marks sum]4 Marks

Find the values of $a$ and $b$ when the polynomial $f(x)=a x^3+3 x^2+b x-3$ is exactly divisible by $(2 x+3)$ and leaves a remainder $-3$ when divided by $(x+2)$.

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Q 18[4 marks sum]4 Marks

Find the values of $p$ and $q$ in the polynomial $f(x)= x^3 - px^2 + 14x -q$, if it is exactly divisible by $(x-1)$ and $(x-2).$

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Q 19[4 marks sum]4 Marks

A polynomial $f(x)v when divided by $(x - 1)$ leaves a remainder $3$ and when divided by $(x - 2)$ leaves a remainder of $1.$ Show that when its divided by $(x - i)(x - 2),$ the remainder is $(-2x + 5).$

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Q 20[4 marks sum]4 Marks

Prove that $(5x - 4)$ is a factor of the polynomial $f(x) = 5x^3 - 4x^2 - 5x +4$. Hence factorize It completely.

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Remainder And Factor Theorems question types

Remainder And Factor Theorems questions

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Remainder And Factor Theorems Mathematics - Remainder And Factor Theorems

Remainder And Factor Theorems question types

Remainder And Factor Theorems questions

Generate a Remainder And Factor Theorems paper free