Factorisation of Quadratic Polynomial

Q.

Factorize $ax+ay-bx-by$

Q. If (x +5) and (x -3) are the factors of $a{x}^2+bx+c,$ , then values of a, b and c are

1. 1, -2, 15
2. 1, 2, -15
3. 1, 2, 15
4. 1, 2, 3

Q.

The zeroes of the polynomial
$P\left(x\right)=a{x}^2+bx+c$ are 1 and 2.
Find the value of $a,b\text{and}c$.

1. a = 1, b = -3 , c = 1

2. a = 1 , b = -3, c = 2

3. a = -1 , b = -3, c = -2

4. a = 3, b = -1, c = 1

Q. If $x-2$ is a factor of each of the following two polynomials, find the value of $a$ in each case

$x^3-2a{x}^2+ax-1$

Q.

How many zeroes do the polynomials
$P_1\left(x\right)=x^3+x^2+x+1$ and
$P_2\left(x\right)=x^2+1$
have in common?

1. 1

2. 2

3. 3

4. 0

Q. Match the polynomials with their respective factors.

Q. In each of the following two polynomials, find the value of $a$, if $x-a$ is a factor:

$x^6-a{x}^5+x^4-a{x}^3+3x-a+2$