GCD by Factorization

Q.

Factorise the following expression: $20l^{2}m+30alm$

Q.

The fifth of the H.P. 2, $\frac{5}{2}$, $\frac{10}{3}$, ................. will be

1. 

2. 

3. 10

4. 

Q. (i) If $a=x^{m+n}{y}^l,b=x^{n+l}{y}^m\mathrm{and}c=x^{l+m}{y}^n$, prove that $a^{m-n}{b}^{n-l}{c}^{l-m}=1$.

(ii) If $x=a^{m+n},y=a^{n+l}\mathrm{and}z=a^{l+m}$, prove that $x^m{y}^n{z}^l=x^n{y}^l{z}^m$.

Q.

H.C.F of $a^2{b}^3$ and $a^3{b}^2{d}^7$ is $a^2{b}^2$. What is their H.C.F

1. $a^2{b}^3$

2. $a^3{b}^2{d}^7$

3. None of the above

4. $a^2{b}^2$

Q. Divide the given polynomial.
8$(x^3{y}^2{z}^2+x^2{y}^3{z}^2+x^2{y}^2{z}^3)$ $÷4x^2{y}^2{z}^2$

1. $2(x-y+z)$
2. $2(x+y-z)$
3. $2(x-y-z)$
4. $2(x+y+z)$

Q. Which of the following is not a way to factorise?

1. Finding common factor
2. Regrouping
3. Splitting the middle term
4. Finding least common mutiple

Q.

Find th H.C.F of $3x{y}^2{z}^3$, $3y{z}^2{x}^2$ and $x^2{y}^{2}z$

1. $x^{2}yz$

2. $3x{y}^2{z}^3$

3. $xyz$

4. $x^2{y}^{2}z$

Q. What is the common factor of the terms in the expression x+xy+3xz?

1. 1
2. y
3. z
4. x

Q. Identify any two factors after factorising the expression $x^3-6x^2+11x-6$. The factors are and .

1. $(x+1)$
2. $(x-1)$
3. $(x+2)$
4. $(x-2)$

Q. Find the product $\left(x+y-z\right)\left(x^2+y^2+z^2-xy+yz+zx\right)$.

Q. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Q. Finding common multiple is one of the ways to factorise an expression.

1. False
2. True

Q. $2xy+3x=x(2y+3x)$
The above factorisation is done by finding the common factor.

1. True
2. False

Q. Which of the following is not a way to factorise?

1. Finding common factor
2. Finding least common mutiple
3. Splitting the middle term
4. Regrouping

Q.

What is the H.C.F of $x^2+2x-8,x^3-4x^2+4x,x^2-4$

1. $x-2$

2. $x+3$

3. $x^2$

4. $x+1$

Q.

HCF of $(x^2-9)$ and $(x+3{)}^2$ is 'a'. HCF of $x^2+x-6$ and $x^2-4$ is 'b'. Then $a\times b$ is ____.

1. $x^2+x-6$

2. $x^2+x-8$

3. $x^2-x-6$

4. $x^3+x-6$

Q.

Find the H.C.F of $16a^2{b}^3{x}^4{y}^5$, $40a^3{b}^2{x}^3{y}^4$ and $24a^5{b}^5{x}^6{y}^4$

1. $16a^2{b}^2{x}^4{y}^4$

2. $24a^5{b}^5{x}^6{y}^4$

3. $40a^3{b}^2{x}^3{y}^4$

4. $8a^2{b}^2{x}^3{y}^4$

Q. If ($x+a$) is a factor of a polynomial f($x$), then f(a) = 0.

1. True
2. False