Polynomials Quiz 8

Find the values of “a” and “b” so that (x + 2) and (x – 1) may be factors of $x^3 + 10x^2 + ax + b$

Simplify $\frac{(x+y)^2-z^2}{(x+y+z)^2}\div\left\{\frac{(x-z)^2-y^2}{x^2+xy+zx}\div\frac{(x-y)^2-z^2}{x^2-xy+zx}\right\}.$

The expression $2x^3 + ax^2 + bx – 2$ leaves a remainder 7 and 0 when divided by $(2x-3)$ and $(x+2)$ Find the values of a and b.

Find the value of k if the expressions $p(x) = kx^3 + 4x^2 + 3x – 4$ and $q(x) = x^3 – 4x + k$ leave the same remainder when divided by $(x-3)$

If a + c + e = 0 and b + d = 0 then $ax^4 + bx^3 +cx^2 + dx + e$ is exactly divisible by ..................

Simplify $\frac{1}{1+x+x^2}-\frac{1}{1-x+x^2}+\frac{2x}{1+x^2+x^4}$ ...............

What should be subtracted from $x^3 – 2x^2 + 4x + 1$

What should be subtracted from $\frac{7x}{x^2-x-12}$ to get $\frac{3}{x+3}$ ?

If $ax^2 + 2a^2 x + b^3$ is divisible by (x + a) then ……………

Which of the following expressions is a rational expression ?