Factorisation of Polynomials

If $a\ne 0$,then find the factors of $a^2-\frac{27}{a}$.
 

If $\left(x-a\right)$ is a factor of $p\left(x\right)=a{x}^2+bx+c$, then $p\left(a\right)=0$. Yes $/$ No.

For what value of $a$ is the polynomial $(2x^3+a{x}^2+11x+a+3)$ exactly divisible by $(2x-1)$?

If $\left(x+1\right)$ is a factor of $\left(x^2-3ax+3a-7\right)$, then find the value of $a$.

A factor of $x^3+16x^2+79x+120$ is

$\left(x-a\right)$ is a factor of $p\left(x\right)=a{x}^2+bx+c$. Which of the following is true?

If $x+1$ is a factor of the polynomial $2x^2+kx$, then the value of $k$ is:

Consider the polynomial$ \text{P}\left(x\right)={x}^{4}+{x}^{3}-4{x}^{2}-2\text{x}+4$.

Two of its factors are $ \left(x-\sqrt{2}\right)$ and $ \left(x+\sqrt{2}\right)$

What are the other two factors of $ \text{P}\left(x\right)$?

$ \text{P}\left(x\right)=(x-1)(x-2)(x-3)$

Which of the following is/are factor(s) of the polynomial, $ \text{P}\left(x\right)$?

(i) $ (x-1)$

(ii) $ (x+1)$

(iii) $ ({x}^{2}-3x+2)$

(iv) $ ({x}^{2}-5x+6)$

(v) $ ({x}^{2}-1)$

Which of the following statements is true about the polynomial, $ \text{P}\left(x\right)$ according to factor theorem?

Which of the following is a factor of the polynomial $ \text{P}\left(x\right)=(-x-2)(x+3)$?

For the polynomial P(x), P (-2) = 0 and P (1) = 0.

Which of the following is definitely a factor of P(x)?

Shown below are some of values of polynomial P(x):

P(-2) = -2, P(0) = 0, P(1) = 1

Which of the following is definitely a factor of P(x)?

If $(x-1)$ divides the polynomial $\left(k{x}^3-2x^2+25x-26\right)$ without remainder, then find the value of $k$.