Factor of Polynomials

Q.

‘p’ and ‘q’ are the zeroes of the polynomial,
$a{x}^2+bx+c=0$
The values of $a$ and $b$ are:

1. -1, -(p + q)

2. 1, p + q

3. 1, -(p+q)

4. None of these

Q.

‘p’ and ‘q’ are the zeroes of the polynomial $a{x}^2+bx+c=0$.

(x-p) and (x-q) are the only factors of the expression $a{x}^2+bx+c$,

The values of $a$ and $b$ are:

1. 1, p + q

2. 1, -(p+q)

3. -1, -(p+q)

4. -1, -(p + q)

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 = 3, b = -1, c = 1

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

Q. Which among the given options is one of the factors of
$x^2+\frac{x}{6}-\frac{1}{6}$?

1. $3x+1$
2. $x-\frac{1}{2}$
3. $x-\frac{1}{5}$
4. $2x+1$

Q. The factorisation of $2y^3+10y^2-48y$ is ____.

1. $2y(y-3)(y+8)$
2. $2y(y+3)(y+8)$
3. $2y(y-3)(y-8)$
4. $2y(y+3)(y-8)$

Q. If both $x-2$ and $x-\frac{1}{2}$ are factors of $p{x}^2+5x+r$, then:

1. 
2. 
3. 
4. 

Q. $x^2+5x-24$ can be factorized as .

1. $(x+3)(x+8)$
2. $(x-3)(x-8)$
3. $(x-3)(x+8)$
4. $(x+3)(x-8)$

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. 0

3. 2

4. 3

Q. Select the factors of ' -46 ' which is a constant in a polynomial.

1. 2
2. 3
3. 5
4. 46
5. 1
6. 7
7. -2
8. -1

Q.

‘p’ and ‘q’ are the zeroes of the polynomial
$a{x}^2+bx+c$. The values of $a$ and $b$ are

1. -1, -(p + q)
2. 1, p + q
3. 1, -(p+q)
4. -1, -(p+q)