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a ) M(x) + N(x) + P(x) = (\(3x^3+x^2+4x^4-x-3x^3+5x^4+x^2-6\)) + (\(-x^2-x^4+4x^3-x^2-5x^3+3x+1+x\)) + (\(1+2x^5-3x^2+x^5+3x^3-x^4-2x\))
= \(3x^3+x^2+4x^4-x-3x^3+5x^4+x^2-6\) \(-x^2-x^4+4x^3-x^2-5x^3+3x+1+x\)\(1+2x^5-3x^2+x^5+3x^3-x^4-2x\)
= ( \(3x^3-3x^3+4x^3-5x^3+3x^3\) ) + ( \(x^2+x^2-x^2-x^2-3x^2\) ) + (\(4x^4+5x^4-x^4-x^4\) ) + ( \(-x+3x+x-2x\) ) + ( \(-6+1+1\) ) + (\(2x^5+x^5\) )
= \(2x^3-3x^2+7x^4+x-4+3x^5\)
a) Ta có: \(A\left(x\right)=2x^5-3x^3+7x-6x^4+2x^3+2\)
\(=2x^5-6x^4-x^3+7x+2\)
Ta có: \(B\left(x\right)=x^5-3x^3+7x-6x^2+x^5+2x^2\)
\(=2x^5-3x^3-4x^2+7x\)
b) Ta có: \(A\left(x\right)-B\left(x\right)\)
\(=2x^5-6x^4-x^3+7x+2-\left(2x^5-3x^3-4x^2+7x\right)\)
\(=2x^5-6x^4-x^3+7x+2-2x^5+3x^3+4x^2-7x\)
\(=-6x^4+2x^3+4x^2+2\)
Ta có: \(A\left(x\right)+B\left(x\right)\)
\(=2x^5-6x^4-x^3+7x+2+2x^5-3x^3-4x^2+7x\)
\(=4x^5-6x^4-4x^3-4x^2+14x+2\)
c) Ta có: C(x)+2A(x)=B(x)
\(\Leftrightarrow C\left(x\right)=B\left(x\right)-2\cdot A\left(x\right)\)
\(\Leftrightarrow C\left(x\right)=2x^5-3x^3-4x^2+7x-2\cdot\left(2x^5-6x^4-x^3-7x+2\right)\)
\(\Leftrightarrow C\left(x\right)=2x^5-3x^3-4x^2+7x-4x^5+12x^4+2x^3+14x-4\)
\(\Leftrightarrow C\left(x\right)=-2x^5+12x^4-x^3-4x^2+21x-4\)
a, P(x)=\(3x^3+2x^2-2x+7-x^2-x\)
=\(3x^3+\left(2x^2-x^2\right)+\left(-2x-x\right)+7\)
=\(3x^3+x^2-3x+7\)
Q(x)=\(-3x^3+x-14-2x-x^2-1\)
= -3x\(^3\)+\((x-2x)\)+(-14-1)-x\(^2\)
= -3x\(^3\)-x -15 -x\(^2\)
b, M(x)=P(x)+Q(x)=\((3x^3+x^2-3x+7)\)+ (-3x\(^3\)-x-15-x\(^2\))
=\(3x^3+x^2-3x+7\) -3x\(^3\) -x -15 -x\(^2\)
=(3x\(^3\)- 3x\(^3\)) + (x\(^2\)-x\(^2\)) + (-3x-x) + (7-15)
= -4x - 8
a, P(x)=3x3+2x2−2x+7−x2−x3x3+2x2−2x+7−x2−x
=3x3+(2x2−x2)+(−2x−x)+73x3+(2x2−x2)+(−2x−x)+7
=3x3+x2−3x+73x3+x2−3x+7
Q(x)=−3x3+x−14−2x−x2−1−3x3+x−14−2x−x2−1
= -3x33+(x−2x)(x−2x)+(-14-1)-x22
= -3x33-x -15 -x22
b, M(x)=P(x)+Q(x)=(3x3+x2−3x+7)(3x3+x2−3x+7)+ (-3x33-x-15-x22)
=3x3+x2−3x+73x3+x2−3x+7 -3x33 -x -15 -x22
=(3x3- 3x3) + (x2-x2) + (-3x-x) + (7-15)
= -4x - 8
\(M\left(x\right)=2x\left(x-3\right)-5\left(x-2\right)+3x^2\)
\(=2x^2-6x-5x+10+3x^2\)
\(=5x^2-11x+10\)
\(N\left(x\right)=-x\left(x+1\right)-\left(2x-4\right)+x^2\left(2x-3\right)\)
\(=-x^2-x-2x+4+2x^3-3x^2\)
\(=2x^3-4x^2-3x+4\)
\(M\left(x\right)-N\left(x\right)-x^2\left(x+6\right)\)
\(=5x^2-11x+10-\left(2x^3-4x^2-3x+4\right)-x^2\left(x+6\right)\)
\(=5x^2-11x+10-2x^3+4x^2+3x-4-x^3-6x^2\)
\(=-3x^3+3x^2-8x+6\)
thanks nha