a, \(P\left(x\right)=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x\)
\(Q\left(x\right)=-x^5+5x^4-2x^3+4x^2-\dfrac{1}{4}\)
b, \(P\left(x\right)+Q\left(x\right)=\left(x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x\right)+\left(-x^5+5x^4-2x^3+4x^2-\dfrac{1}{4}\right)\)
\(=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x-x^5+5x^4-2x^3+4x^2-\dfrac{1}{4}\)
\(=\)\(\left(x^5-x^5\right)+\left(7x^4+5x^4\right)+\left(-9x^3-2x^3\right)+\left(-2x^2+4x^2\right)-\dfrac{1}{4}x-\dfrac{1}{4}\)
\(=12x^4-11x^3+2x^2-\dfrac{1}{4}x-\dfrac{1}{4}\)
\(P\left(x\right)-Q\left(x\right)=\left(x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x\right)-\left(-x^5+5x^4-2x^3 +4x^2-\dfrac{1}{ }\right)\)
\(=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x+x+5x^4+2x^3-4x^2+\dfrac{1}{4}\)
\(=\left(x^5+x^5\right)+\left(7x^4-5x^4\right)+\left(-9x^3+2x^5\right)+\left(-2x^2-4x^2\right)-\dfrac{1}{4}x+\dfrac{1}{4}\)
\(=2x^5+2x^4-7x^3-6x^2-\dfrac{1}{4}x+\dfrac{1}{4}\)
-Chúc bạn học tốt-
