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\(A\left(x\right)+B\left(x\right)=3x^4-\frac{3}{4}x^3+2x^2-3+8x^4+\frac{1}{5}x^3-9x+\frac{2}{5}\)
\(=11x^4-\frac{11}{20}x^3+2x^2-\frac{13}{5}-9x\)
\(A\left(x\right)-B\left(x\right)=3x^4-\frac{3}{4}x^3+2x^2-3-8x^4-\frac{1}{5}x^3+9x-\frac{2}{5}\)
\(=-5x^4-\frac{19}{20}x^3+2x^2-\frac{17}{5}+9x\)
Bn làm nót nhé, tương tự thôi
\(A\left(x\right)+B\left(x\right)\)
\(=\left(3x^4-\frac{3}{4}x^3+2x^2-3\right)+\left(8x^4+\frac{1}{5}x^3-9x+\frac{2}{5}\right)\)
\(=11x^4-\frac{11}{20}x^3+2x^2-9x-\frac{13}{5}\)
\(A\left(x\right)-B\left(x\right)\)
\(=3x^4-\frac{3}{4}x^3+2x^2-3-8x^4-\frac{1}{5}x^3+9x-\frac{2}{5}\)
\(=-5x^4-\frac{19}{20}x^3+2x^2+9x-\frac{17}{5}\)
\(B\left(x\right)-A\left(x\right)\)
\(=8x^4+\frac{1}{5}x^3-9x+\frac{2}{5}-3x^4+\frac{3}{4}x^3+2x^2-3\)
\(=5x^4+\frac{19}{20}x^3+2x^2-9x-\frac{13}{5}\)
Bài 5:
a: \(P\left(x\right)=3x^5+x^4-2x^2+2x\)
\(Q\left(x\right)=-3x^5+2x^2-2x+3\)
b: \(P\left(x\right)+Q\left(x\right)=3x^5-3x^5+x^4-2x^2+2x^2+2x-2x+3\)
\(=x^4+3\)
\(P\left(x\right)-Q\left(x\right)=3x^5+x^4-2x^2+2x+3x^5-2x^2+2x-3\)
\(=6x^5+x^4-4x^2+4x-3\)
c: \(P\left(0\right)=3\cdot0^5+0^4-2\cdot0^2+2\cdot0=2\)
\(Q\left(0\right)=-3\cdot0^5+2\cdot0^2-2\cdot0+3=3\)
Vậy: x=0 là nghiệm của P(x), không là nghiệm của Q(x)
bài 1
a) \(-\frac{1}{3}xy\).(3\(x^2yz^2\))
=\(\left(-\frac{1}{3}.3\right)\).\(\left(x.x^2\right)\).(y.y).\(z^2\)
=\(-x^3\).\(y^2z^2\)
b)-54\(y^2\).b.x
=(-54.b).\(y^2x\)
=-54b\(y^2x\)
c) -2.\(x^2y.\left(\frac{1}{2}\right)^2.x.\left(y^2.x\right)^3\)
=\(-2x^2y.\frac{1}{4}.x.y^6.x^3\)
=\(\left(-2.\frac{1}{4}\right).\left(x^2.x.x^3\right).\left(y.y^2\right)\)
=\(\frac{-1}{2}x^6y^3\)
Bài 3:
a) \(f\left(x\right)=-15x^2+5x^4-4x^2+8x^2-9x^3-x^4+15-7x^3\)
\(f\left(x\right)=\left(5x^4-x^4\right)-\left(9x^3+7x^3\right)-\left(15x^2+4x^2-8x^2\right)+15\)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
b)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
\(f\left(1\right)=4\cdot1^4-16\cdot1^3-11\cdot1^2+15\)
\(f\left(1\right)=4\cdot1^4-16\cdot1^3-11\cdot1^2+15\)
\(f\left(1\right)=-8\)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
\(f\left(-1\right)=4\cdot\left(-1\right)^4-16\cdot\left(-1\right)^3-11\cdot\left(-1\right)^2+15\)
\(f\left(-1\right)=24\)
a)Sắp xếp : \(f\left(x\right)=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x\)
\(g\left(x\right)=-x^5+5x^4-2x^3+4x^2-\dfrac{1}{4}x\)
Ta có : \(f\left(x\right)+g\left(x\right)=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x-x^5+5x^4-2x^3+4x^2-\dfrac{1}{4}x\)
\(=12x^4-11x^3+2x^2-\dfrac{1}{2}x\)
\(f\left(x\right)-g\left(x\right)=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x+x^5-5x^4+2x^3-4x^2+\dfrac{1}{4}x\)
\(=2x^5+2x^4-7x^3-6x^2\)
1) \(A\left(x\right)=-5x^3+3x^4+\frac{5}{7}-8x^2-10x\)
\(A\left(x\right)=3x^4-5x^3-8x^2-10x+\frac{5}{7}\)
\(B\left(x\right)=-2x^4-\frac{2}{7}+7x^2+8x^3+6x\)
\(B\left(x\right)=-2x^4+8x^3+7x^2+6x-\frac{2}{7}\)
2) \(A\left(x\right)=3x^4-5x^3-8x^2-10x+\frac{5}{7}\)
+
\(B\left(x\right)=-2x^4+8x^3+7x^2+6x-\frac{2}{7}\)
\(A\left(x\right)+B\left(x\right)=x^4+3x^3-x^2-4x+\frac{3}{7}\)
\(A\left(x\right)=3x^4-5x^3-8x^2-10x+\frac{5}{7}\)
-
\(B\left(x\right)=-2x^4+8x^3+7x^2+6x-\frac{2}{7}\)
\(A\left(x\right)-B\left(x\right)=5x^4-13x^3-15x^2-16x+1\)