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a) Ta có:
\(P\left(x\right)=x-2x^2+3x^5+x^4+x=3x^5+x^4-2x^2\)
\(Q\left(x\right)=3-2x-2x^2+x^4-3x^5-x^4+4x^2\)
\(=-3x^5+2x^2-2x+3\)
b) Ta có:
\(P\left(x\right)+Q\left(x\right)=3x^5+x^4-2x^2-3x^5+2x^2-2x+3\)
\(=x^4-2x+3\)
\(P\left(x\right)-Q\left(x\right)=3x^5+x^4-2x^2+3x^5-2x^2+2x-3\)
\(=6x^5+x^4-4x^2+2x-3\)
c) Ta có: \(P\left(0\right)=3.0^5+0^4-2.0^2=0\)
=> x = 0 là nghiệm của P(x)
Mà \(Q\left(0\right)=-3.0^5+2.0^2-2.0+3=3\)
=> x = 0 không là nghiệm của đa thức Q(x)
a: P(x)=6x^4+5x^3-3x^2+5x-10
Q(x)=5x^4+5x^3+2x^2-4x+4
b: P(x)+Q(x)
=6x^4+5x^3-3x^2+5x-10+5x^4+5x^3+2x^2-4x+4
=11x^4+10x^3-x^2+x-6
P(x)-Q(x)
=6x^4+5x^3-3x^2+5x-10-5x^4-5x^3-2x^2+4x-4
=x^4-5x^2+9x-14
a: \(P\left(x\right)=x-2x^2+3x^5+x^4+x-1\)
\(=3x^5+x^4-2x^2+2x-1\)
\(Q\left(x\right)=3-2x-2x^2+x^4-3x^5-x^4+4x^2\)
\(=-3x^5+2x^2-2x+3\)
b: P(x)+Q(x)
\(=3x^5+x^4-2x^2+2x-1-3x^5+2x^2-2x+3\)
\(=x^4+2\)
P(x)-Q(x)
\(=3x^5+x^4-2x^2+2x-1+3x^5-2x^2+2x-3\)
\(=6x^5+x^4-4x^2+4x-4\)
a: \(P\left(x\right)=3x^5+5x-4x^4-2x^3+6+4x^2\)
\(=3x^5-4x^4-2x^3+4x^2+5x+6\)
\(Q\left(x\right)=2x^4-x+3x^2-2x^3+\frac14-x^5\)
\(=-x^5+2x^4-2x^3+3x^2-x+\frac14\)
b: P(x)+Q(x)
\(=3x^5-4x^4-2x^3+4x^2+5x+6-x^5+2x^4-2x^3+3x^2-x+\frac14\)
\(=2x^5-2x^4-4x^3+7x^2+4x+6,25\)
P(x)-Q(x)
\(=3x^5-4x^4-2x^3+4x^2+5x+6+x^5-2x^4+2x^3-3x^2+x-\frac14\)
\(=4x^5-6x^4+x^2+6x+5,75\)
c: \(P\left(-1\right)=3\cdot\left(-1\right)^5-4\cdot\left(-1\right)^4-2\cdot\left(-1\right)^3+4\cdot\left(-1\right)^2+5\cdot\left(-1\right)+6\)
=-3-4+2+4-5+6
=-7+6-5+6
=12-12
=0
=>x=-1 là nghiệm của P(x)
\(Q\left(-1\right)=-\left(-1\right)^5+2\cdot\left(-1\right)^4-2\cdot\left(-1\right)^3+3\cdot\left(-1\right)^2-\left(-1\right)+\frac14\)
\(=1+2+2+3+1+\frac14=9,25>0\)
=>x=-1 không là nghiệm của Q(x)
a)
\(P\left(x\right)=x-2x^2+3x^5+x^4+x\)
\(\Leftrightarrow P\left(x\right)=\left(x+x\right)-2x^2+x^4+3x^5\)
\(\Leftrightarrow P\left(x\right)=2x-2x^2+x^4+3x^5\)
\(Q\left(x\right)=3-2x-2x^2+x^4-3x^5-x^4+4x^2\)
\(\Leftrightarrow Q\left(x\right)=3-2x+\left(-2x^2+4x^2\right)+\left(x^4-x^4\right)-3x^5\)
\(\Leftrightarrow Q\left(x\right)=3-2x+2x^2-3x^5\)
b)
\(P\left(x\right)+Q\left(x\right)=\left(2x-2x^2+3x^5+x^4\right)+\left(3-2x+2x^2-3x^5\right)\)
\(=2x-2x^2+3x^5+x^4+3-2x+2x^2-3x^5\)
\(=\left(2x-2x\right)+\left(3x^5-3x^5\right)+\left(-2x^2+2x^2\right)+x^4+3\)
\(=x^4+3\)
\(P\left(x\right)-Q\left(x\right)=\left(2x-2x^2+3x^5+x^4\right)-\left(3-2x+2x^2-3x^5\right)\)
\(=2x-2x^2+3x^5+x^4-3+2x-2x^2+3x^5\)
\(=\left(2x+2x\right)+\left(-2x^2-2x^2\right)+\left(3x^5+3x^5\right)+x^4-3\)
\(=4x-4x^2+6x^5+x^4-3\)
\(=6x^5+x^4-4x^2+4x-3\)
c)
\(P\left(x\right)=P\left(0\right)=0-2.0^2+3.0^5+0^4+0=0-0+0+0+0=0\)
\(Q\left(x\right)=Q\left(0\right)=3-2.0-2.0^2+0^4-3.0^5-0^4+4.0^2=3-0-0+0-0-0+0=3\)