What is the remainder, when $$4x^{4}+10x^{3}-20x^{2}+90$$ is divided by $$(x+2)$$ ?
By Remainder theorem, when $$f(x)$$ is divided by $$x+a$$ then the remainder is $$f(-a)$$
Let $$f\left(x\right)=4x^4+10x^3-20x^2+90$$
Required Remainder = $$f\left(-2\right)=4\left(-2\right)^4+10\left(-2\right)^3-20\left(-2\right)^2+90=4\times16\ +10\left(-8\right)-20\times4\ +90=\ 64-80-80+90=-6$$
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