Factorisation of a Polynomial

Q.

What's the difference between remainder theorem and factor theorem?

Q.

Common factor in quadratic polynomials $x{}^2+8x+15$ and $x^2+3x-10$ is

Q.

Factorise $3x^2-x-4$.

Q. Let p(x) be a fourth degree polynomial with coefficient of leading term 1and p(1)=p(2)=p(3)=0, then find the value ofp(0)+p(4).

Q.

Factorize: x³ + x² - 17x + 15

Q.

If (x - 2 ) is a factor of the polynomial x² - 3x + 5a , find the value of ‘a’

1. a = 2/5

2. a = -2/5

3. a = 5/2

4. a =3/5

Q.

FIND THE VALUE OF a IF x-a IS A FACTOR OF x^{​​​​​​3} - ax^{​​​​​2} - 2x + a-1

Q.

Find the values of a and b so that(x-1) and (x+1) are the factors of x⁴+ax³-3x²+2x+b

Q.

check whether g(x) is a factor of p(x)

p(x)= 8x³-6x²-4x+3

g(x)= x/3-1/4

Q. 15. If (x-3) is a factor of X3+ax2+bx+18 and a+b=-7.Find a and b

Q.

Let $f\left(x\right)=x^3+k{x}^2+hx+6$.What are the values of $h$ and $k$ so that $(x+1)$ and $(x–2)$ are factors of $f\left(x\right)$?

1. $h=1,k=-4$

2. $h=-4,k=1$

3. $h=4,k=-1$

4. $h=-1,k=-4$

Q.

If (x-1) is a factor of ax - a, then find the value of a

1. a = 1

2. a = 2

3. a = 3

4. All values of a

Q.

Find the value of k, If x+k is a factor of the polynomials:

x^4-k^2x^2+3x-6k.

Q.

If (x+1) and (x-1) are factors of mx³ +x² - 2x +n find the value of m and n

Q.

Factorize: $2x^2+7x+3$

Q. What is the differencre between remainder theorem and factor theorem?

Q.

If $(2x+5)$ is a factor of $2x^2-k$, then the value of $k$ is.

1. 25

2. $\frac{25}{2}$

3. -1

4. 2

Q.

One of the factors of (16y² - 1) + (1 -4y)² is

1. (4+y)

2. (4y+1)

3. 8y

4. (4-y)

Q.

Find the value of $p\left(x\right)$ for $x=1$ if $p\left(x\right)$ has $(x–1)$ a factor.

1. $1$

2. $-1$

3. $0$

4. $2$

Q.

The value of p for which x + p is a factor of x² + px + 3 - p is:

1. -3

2. 1

3. -1

4. 3

Q.

If (x-2) is the factor of x² + 2x+ a, find the value of 'a'.

1. a = 16

2. a = -8

3. a = 8

4. a = -16

Q.

Find the value of p(2) if p(x) has (x-2) as its factor.

1. 2

2. 0

3. 3

4. -2

Q.

What are the two factors of quadratic polynomial x² – 16x + 64?

1. (x+8) and (x-8)

2. (x-16) and (x-64)

3. (x+16) and (x-4)

4. (x-8) and (x-8)

Q.

If both (x+2) and (2x-1) are the factors of ax² + 5x +b, show that a- b=0

Q.

Factorize the following expression:

$ax-5b+ab-5x$

Q. The remainder when a polynomial p(x) is divided by one of its factors is ______.

1. 1
2. 0
3. 2
4. 3

Q. What are factor and remainder theorem ?

Q.

2x^2_13x+18

Q.

If $x+a$ is the HCF of $x^2+px+q$ and $x^2+1x+m$, then find the value of $a$.

Q.

x+1 is a factor of p(x)= x³+3x²+3x+1 , so what is the value of p(-1)

1. -1

2. 1

3. 0

4. 2