Polynomials Quiz 7

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

The value of $6a + 11b$ if $x^3 – 6x^2 + ax + b$ is exactly divisible by $(x^2 – 3x + 2)$ is ......

If $4x^4 -(a – 1) x^3 + ax^2 – 6x – 1$ is divisible by $2x – 1$, the value of a ……

If f(x) = $x^2 + 5x + p$ and g(x) = $x^2 + 3x + q$ have a common factor then $(p – q)^2 = ……$

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

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

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

If $\alpha, \beta, \gamma$ are the zeroes of $3x^3 – 5x^2 – 11x – 3$ then $\alpha+ \beta+ \gamma$ = .........

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