Factors of Algebraic Expressions and Factorisation

Q. $Divide\left(24x{y}^2{z}^3\right)by\left(6y{z}^2\right).$

1. $4x{y}^{2}z$
2. $4x{y}^2{z}^2$
3. $4xyz$
4. $4x{y}^2$

Q.

Factorise $x^6-y^6$ Solve This.

Q.

Verify whether the following value is the zero of the polynomial, indicated against them:

$p\left(x\right)=2x+1$, $x=\frac{1}{2}$.

Q. Factorize the following expression:

$16a^4-b^4$

Q.

Multiply the binomials: $\left(\frac{3}{4}{a}^2+3b^2\right)$ and $4\left(a^2-\frac{2}{3}{b}^2\right)$

Q.

Verify that $3,-1,\frac{-1}{3}$are the zeros of cubic polynomial $p\left(x\right)=3x^3-5x^2-11x-3$.

Q. Which of the following are the factors of the expression $ax-ay+by-bx$?

1. $a$, $b$, $x$, and $y$
2. $a$, $b$
3. $(a-b)$ and $(x-y)$
4. $(a+b)$ and $(x-y)$

Q. Question 25

An irreducible factor of $24x^2{y}^2$ is
(a) $x^2$
(b) $y^2$
(c) $x$
(d) $24x$

Q.

Factorise the following expression: $-4a^2+4ab-4ac$

Q.

Factorize the following expression:

$4(x+y)-6{(x+y)}^2$

Q.

What is the HCF of $a^2$ $b^3$ $c^2$, b$c^3$, a$c^2$ ?

1. $b^2$

2. $c^3$

3. $c^2$

4. c

Q.

If the HCF and the LCM of the polynomial are $x^2$ - 1, $x^4$ - 1 respectively. Find out the uncommon factor of the two polynomials.

1. x + 1

2. x - 1

3. x

4. $x^2$ + 1

Q. Question 3
Find and correct the errors in the statement : $2x+3y=5xy$

Q. Factorise:
p² − 10p + 25

Q.

Find the greatest common factors (GCF / HCF) of the following polynomials :

$4a^2{b}^3,-12a^{3}b,18a^4{b}^3$

Q.

Express as the product of three factors.

$42=\_\_\_\_\_\_\_\_$

Q.

Factorise the following expressions

(i) 7x − 42

(ii) 6p − 12q

(iii) 7a² + 14a

(iv) −16z + 20z³

(v) 20l²m + 30 alm

(vi) 5x²y − 15xy²

(vii) 10a² − 15b² + 20c²

(viii) −4a² + 4ab − 4 ca

(ix) x²yz + xy²z + xyz²

(x) ax²y + bxy² + cxyz

Q.

Find the greatest common factors (GCF / HCF) of the following polynomials :

$6x^{3}y\text{and}18x^2{y}^3$

Q.

Find the greatest common factors (GCF / HCF) of the following polynomials :

$a^2{b}^3,a^3{b}^2$

Q.

Find the greatest common factors (GCF / HCF) of the following polynomials :

$9x^2,15x^2{y}^3,6x{y}^2\text{and}21x^2{y}^2$

Q.

Factorise the following expression: $x^{2}yz+x{y}^{2}z+xy{z}^2$

Q. Factorize the following expression:

$a^4-16(b-c{)}^4$

Q. Find the number of factors of 18.

1. 3
2. 8
3. 6
4. 4

Q. Factorize the following algebraic expression: $a^2+2a-3$

Q.

Question 3 (iii)
Is $43.\overline{123446789}$ rational or not. If it is rational, and of the form $\frac{p}{q}$, what can you say about the prime factors of q?

Q. Factorise :
$\left(i\right)16a^2–\frac{25}{4a^2}$
$\left(ii\right)16a^{2}b–\frac{b}{16a^2}$
$\left(iii\right)100(x+y{)}^2–81(a+b{)}^2$
$\left(iv\right)(x–1{)}^2–(x–2{)}^2$

Q.

Factorized form of $18mn+10mnp$ is ________.

Q.

Find the greatest common factors (GCF / HCF) of the following polynomials :

$2x^2\text{and}12x^2,$

Q.

Find the greatest common factors (GCF / HCF) of the following polynomials :

$x^3,-y{x}^2$

Q.

Find the greatest common factors (GCF / HCF) of the following polynomials :

$36a^2{b}^2{c}^4,54a^5{c}^2,90a^4{b}^2{c}^2$