Chhi Phuong
10/08/2017 at 21:52-
a) \(f\left(x\right)=10x^5-8x^4+6x^3-4x^2+2x+2\)
\(g\left(x\right)=-5x^5+4x^4-3x^3+3x^2-5x+2\)
\(h\left(x\right)=-x^5+2x^4-x^3+x-7\)
\(f\left(x\right)+g\left(x\right)-h\left(x\right)=6x^5-6x^4+4x^3-x^2-4x+11\)
\(f\left(x\right)-g\left(x\right)-h\left(x\right)=16x^5-14x^4+10x^3-7x^2+6x+7\)
The degrees of 2 polynomials are both 5
b) \(f\left(x\right)+2g\left(x\right)=0\)
\(\Leftrightarrow10x^5-8x^4+6x^3-4x^2+2x+2+2\left(-5x^5+4x^4-3x^3+3x^2-5x+2\right)=0\)
\(\Leftrightarrow2x^2-8x+6=0\Leftrightarrow x^2-4x+3=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
P/S : I forgot the way to translate "hệ số tự do" and "hệ số cao nhất" into English. I'll come back soon