For the expression f(x) =  $x^3+a{x}^2+bx+cx^3+ax^2+bx+c$ if f(1) = f(2) = 0 and f(4) = f(0). Find the values of a, b, c.

If $(x^4+a{x}^3-7x^2-8x+b)(x^4+ax^3-7x^2-8x+b)$ is completely divisible by $(x^2+5x+6)(x^2+5x+6)$. Then the values of a and b are ................

$x^3+2x^2+ax+bx^3+2x^2+ax+b$ is exactly divisible by $(x^2-1)(x^2-1)$ . The values of a and b is …………

Find the remainder when $x^4+15x^3+6x^2+12x+3x^4+15x^3+6x^2+12x+3$ is divided by x + 2 ? ……………

If $x^2+x-1x^2\; +\; x\; -1$ is a factor of x4 + $p{x}^3+q{x}^2\text{–}1px^3\; +\; qx^2\; –\; 1$ then the values of p and q can be …………

If the zeroes of the rational expression (ax + b) (3x + 2) are $\frac{-2}{3}\backslash frac\{-2\}\{3\}$ and $\frac{1}{2}\backslash frac\{1\}\{2\}$ then a + b = …………

Simplify $\frac{x+1}{x-1}+\frac{x-1}{x+1}-\frac{2x^2-2}{x^2+1}\backslash frac\{x+1\}\{x-1\}+\backslash frac\{x-1\}\{x+1\}-\backslash frac\{2x^2-2\}\{x^2+1\}$

Find f(4),f(-5),f (3.2) if $f(x)=6.2x^2\text{–}4x^3+4.28\dots \dots f\; (x)\; =\; 6.2x^2\; –\; 4x^3\; +\; 4.28\; \dots \dots$

The product of $x^3+2x^2\text{–}3x+4x^3\; +\; 2x^2\; –\; 3x\; +\; 4$ and $2x^2\text{–}5x+12x^2\; –\; 5x\; +\; 1$ is .........

If A = $\frac{x-1}{x+1}\backslash frac\{x-1\}\{x+1\}$ then 2A – $\frac{1}{2A}\backslash frac\{1\}\{2A\}$