Factorization - ICSE STD 10 Mathematics Questions

Q 1[1 Mark Question Answer]1 Mark

Find the value of a , if $(x - a)$ is a factor of $x^3 - a^2x + x + 2$.

View full solution →

Q 2[1 Mark Question Answer]1 Mark

Find the value of $p$ if the division of $px^3 + 9x^2 + 4x - 10 by (x + 3)$ leaves the remainder $5$.

View full solution →

Q 3[1 Mark Question Answer]1 Mark

When $x^3 + 3x^2– kx + 4$ is divided by $(x – 2)$, the remainder is $k$. Find the value of $k$.

View full solution →

Q 4[1 Mark Question Answer]1 Mark

If $x – 2$ is a factor of $2x^3 - x^2 - px - 2$.
Find the value of $p$

View full solution →

Q 5[1 Mark Question Answer]1 Mark

Use remainder theorem and find the remainder when the polynomial $g(x) = x^3 + x^2 – 2x + 1$ is divided by $x – 3$.

View full solution →

Q 6[2 Mark Question Answer]2 Marks

If the polynomials $a x^3+4 x^2+3 x-4$ and $x^3-4 x+$ a leave the same remainder when divided by $(x-3)$, find the value of $a$.

View full solution →

Q 7[2 Mark Question Answer]2 Marks

Find the remainder when the polynomial $f(x) = 2x^4- 6x^3 + 2x^2 - x + 2$ is divided by $x + 2.$

View full solution →

Q 8[2 Mark Question Answer]2 Marks

Use the factor theorem to factorise completely $x^3 + x^2 - 4x - 4$.

View full solution →

Q 9[2 Mark Question Answer]2 Marks

Use the factor theorem to determine that $x - 1$ is a factor of $x^6 - x^5 + x^4 - x^3 + x^2 - x + 1.$

View full solution →

Q 10[2 Mark Question Answer]2 Marks

In the following problems use the factor theorem to find if g(x) is a factor of $p(x):$
$p(x) = x^3 + x^2 + 3x + 175$ and $g(x) = x + 5.$

View full solution →

Q 11[3 marks sum]3 Marks

Using factor theorem, show that $(x - 3)$ is a factor of $x^3 - 7x^2 + 15x - 9$, Hence, factorise the given expression completely.

View full solution →

Q 12[3 marks sum]3 Marks

Show that $2x + 7$ is a factor of $2x^3 + 5x^2 - 11 x - 14.$ Hence factorise the given expression completely, using the factor theorem.

View full solution →

Q 13[3 marks sum]3 Marks

Show that $x^2 - 9$ is factor of $x^3 + 5x^2 - 9x - 45.$

View full solution →

Q 14[3 marks sum]3 Marks

Find the value of a and b so that the polynomial $x^3 - ax^2 - 13x + b$ has $(x - 1) (x + 3)$ as factor.

View full solution →

Q 15[3 marks sum]3 Marks

If $x – 2$ is a factor of $2x^3 - x^2 - px - 2.$
with the value of p, factorize the above expression completely.

View full solution →

Q 16[5 marks sum]5 Marks

The expression $2 x^3+a x^2+b x-2$ leaves the remainder $7$ and $0$ when divided by $(2 x-3)$ and $(x+2)$ respectively calculate the value of $a$ and $b$. With these value of $a$ and $b$ factorise the expression completely.

View full solution →

Q 17[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 18[4 marks sum]4 Marks

Find the value of the constant a and b, if $(x – 2)$ and $(x + 3)$ are both factors of expression $x^3 + ax^2 + bx - 12.$

View full solution →

Q 19[4 marks sum]4 Marks

The expression $2x^3 + ax^2 + bx - 2$ leaves the remainder $7$ and $0$ when divided by $(2x - 3)$ and $(x + 2)$ respectively calculate the value of $a$ and $b$. With these value of $a$ and $b$ factorise the expression completely.

View full solution →

Factorization question types

Factorization questions

Generate a Factorization paper free

Factorization Mathematics - Factorization

Factorization question types

Factorization questions

Generate a Factorization paper free