GCD of Polynomials

Q. Find the GCD of the given polynomials:

$x^4-1,x^3-11x^2+x-11$

Q. Find the H.C.F. of $(6m^3-17m^2-5m+6)$ and $(6m^3-5m^2-3m+2)$ by using the division method.

1. $6m^2+m-2$
   
2. $6m^2+m+2$
3. $6m^2-m-2$
4. $6m^2-m+2$

Q. The H.C.F. of $x^3-3x^2+x-3$ and $x^4+6x^2+5$ is .

1. $x^4+6x^2+5$
2. $x+3$
3. $x-3$
4. $x^2+1$

Q. Match the expressions on the left side with their HCF given on the right side.

1. $x+3$
2. $x-2$
3. $x-3$
4. $x^2{y}^2$

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

1. $16a^2{b}^2{x}^4{y}^4$
2. $8a^2{b}^2{x}^3{y}^4$
3. $24a^5{b}^5{x}^6{y}^4$
4. $40a^3{b}^2{x}^3{y}^4$

Q.

Find the H.C.F. of $x^3-3x^2+x-3$ and $x^4+6x^2+5.$

1. $x^4+6x^2+5$

2. $x+3$

3. $x-3$

4. $x^2+1$

Q. The H.C.F. of $x^2+2x-8,x^3-4x^2+4x$ and $x^2-4$ is .

1. $x-2$
2. $x+3$
3. $x^2$
4. $x+1$

Q. The H.C.F. of $3x{y}^2{z}^3$, $3y{z}^2{x}^2$ and $x^2{y}^{2}z$ is .

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

Q. Find the GCD of $(a^3-4a^2+7a-6)$ and $(a^3-5a^2+10a-8)$ by using the division method.

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

Q. When two polynomials of same degree has to be divided, ____ should be consider to fix the divisor and dividend.

1. Number of terms
2. constant of the polynomial
3. None of the above
4. coefficient