Polynomials Quiz 6

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

The rational expression A = $\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}-\frac{4x}{x^2+1}\right)$ is multiplied with the additive inverse of B = $\frac{1-x^4}{4x}$ to get C, then C = ……………

The product of $\frac{x^2-4}{3-x}$ and additive inverse of $\frac{x^2-9}{2+x}.$

If (x – 1) and (x + 3) are the factors of $x^3 + 3x^2 – x – 3$ then the other factor is ……

A rational expression whose numerator is a quadratic polynomial with zeroes, 1 and 2 and whose denominator is monomial with zero 3 is ………………

Simplify $\frac{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3}{(a-b)^3+(b-c)^3+(c-a)^3}$

Find "a" and “b” in order that $x^3 – 6x^2 + ax + b$ may be exactly divisible by $x^2 – 3x + 2.$

If g(x) $= x^6 + 3x^4 – 24x^2 + 3$ find g(1), g(2) and g(3).

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

If ‘a’ and ‘b’ are unequal and $x^2 + ax + b$ and $x^2 +bx + a$ have a common factor, then a + b = ……………