Find the quadratic polynomial in x, which when divided by (x – 1) (x – 2) and (x – 3) leaves remainders of 11, 22 and 37 ……………

The sum of $\left(\frac{x-1}{x+1}\right)\backslash left(\backslash frac\{x-1\}\{x+1\}\backslash right)$ and its reciprocal is ……………

The value of $6a+11b6a\; +\; 11b$ if $x^3\text{–}6x^2+ax+bx^3\; –\; 6x^2\; +\; ax\; +\; b$ is exactly divisible by $(x^2\text{–}3x+2)(x^2\; –\; 3x\; +\; 2)$ is ......

If $4x^4-(a\text{–}1)x^3+a{x}^2\text{–}6x\text{–}14x^4\; -(a\; –\; 1)\; x^3\; +\; ax^2\; –\; 6x\; –\; 1$ is divisible by $2x\text{–}12x\; –\; 1$, the value of a ……

If f(x) = $x^2+5x+px^2\; +\; 5x\; +\; p$ and g(x) = $x^2+3x+qx^2\; +\; 3x\; +\; q$ have a common factor then $(p\text{–}q{)}^2=\dots \dots (p\; –\; q)^2\; =\; \dots \dots$

If (x – 4) is the HCF of $p(x)=x^2\text{–}nx-12p(x)\; =\; x^2\; –\; nx\; -12$ and $q(x)=x^2\text{–}mx\text{–}8q(x)\; =\; x^2\; –\; mx\; –\; 8$ then the simplest form of $\frac{p(x)}{q(x)}\backslash frac\{p(x)\}\{q\{(x)\}\}$

Simplify $\frac{x^2-(y-2z{)}^2}{x-y+2z}+\frac{y^2-(2x-z{)}^2}{y+2x-z}+\frac{z^2-(x-2y{)}^2}{z-x+2y}\backslash frac\{x^2-(y-2z)^2\}\{x-y+2z\}+\backslash frac\{y^2-(2x-z)^2\}\{y+2x-z\}+\backslash frac\{z^2-(x-2y)^2\}\{z-x+2y\}$ is ……………

If P= $\frac{1+2x}{1-2x}\backslash frac\{1+2x\}\{1-2x\}$ and Q = $\frac{1-2x}{1+2x}\backslash frac\{1-2x\}\{1+2x\}$ then $\frac{P-Q}{P+Q}\backslash frac\{P-Q\}\{P+Q\}$ = …………

If $\alpha ,\beta ,\gamma \backslash alpha,\; \backslash beta,\; \backslash gamma$ are the zeroes of $3x^3\text{–}5x^2\text{–}11x\text{–}33x^3\; –\; 5x^2\; –\; 11x\; –\; 3$ then $\alpha +\beta +\gamma \backslash alpha+\; \backslash beta+\; \backslash gamma$ = .........

If $x^4\text{–}2x^3+3x^2\text{–}mx+5x^4\; –\; 2x^3\; +\; 3x^2\; –\; mx\; +\; 5$ is exactly divisible by $(x\text{–}3)(x\; –\; 3)$ then m = ……