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f(x) + g(x) - h(x) = (x5 - 4x3 + x2 - 2x + 1) + (x5 - 2x4 + x2 - 5x + 3) - (x4 - 3x2 + 2x - 5)
= x5 - 4x3 + x2 - 2x + 1 + x5 - 2x4 + x2 - 5x + 3 - x4 + 3x2 - 2x + 5
= (x5 + x5) - (2x4 + x4) - 4x3 + ( x2 + x2 + 3x2) - (2x + 5x + 2x) + (1 + 3 + 5)
= 2x5 - 3x4 - 4x3 + 5x2 - 9x + 9
f(x)=
f(x) + g(x) - h(x) = (x5 - 4x3 + x2 - 2x + 1) + (x5 - 2x4 + x2 - 5x + 3) - (x4 - 3x2 + 2x - 5)
= x5 - 4x3 + x2 - 2x + 1 + x5 - 2x4 + x2 - 5x + 3 - x4 + 3x2 - 2x + 5
= (x5 + x5) - (2x4 + x4) - 4x3 + ( x2 + x2 + 3x2) - (2x + 5x + 2x) + (1 + 3 + 5)
= 2x5 - 3x4 - 4x3 + 5x2 - 9x + 9
f(x) + g(x)
= (x5 - 3x2 + 7x4 - 9x3 + x2 - 1/4x) + (5x4 - x5 +x2 - 2x3 + 3x2 - 1/4)
= x5 - 3x2 + 7x4 - 9x3 + x2 - 1/4x + 5x4 - x5 +x2 - 2x3 + 3x2 - 1/4
=12x4 - 11x3 + 2x2 - 1/4x - 1/4
f(x) - g(x)
= (x5 - 3x2 + 7x4 - 9x3 + x2 - 1/4x) - (5x4 - x5 +x2 - 2x3 + 3x2 - 1/4)
= = x5 - 3x2 + 7x4 - 9x3 + x2 - 1/4x - 5x4 + x5 - x2 + 2x3 - 3x2 + 1/4
= 2x5 + 2x4 - 7x3 - 6x2 - 1/4x + 1/4
a) \(f\left(x\right)=5x^3-7x^2+x+7+4x^5\)
\(f\left(-1\right)=5.\left(-1\right)^3-7.\left(-1\right)^2+\left(-1\right)+7+4.\left(-1\right)^5\)
\(f\left(-1\right)=\left(-5\right)-7+\left(-1\right)+7+\left(-4\right)\)
\(f\left(-1\right)=-10\)
\(\Rightarrow f\left(x\right)=-10\)
\(g\left(x\right)=4x^5-3x^3-7x^2+2x+5\)
\(g\left(0\right)=4.0^5-3.0^3-7.0^2+2.0+5\)
\(g\left(0\right)=5\)
\(\Rightarrow g\left(x\right)=0\)
\(h\left(x\right)=x^2-4x-5\)
\(h\left(-\frac{1}{2}\right)=\left(-\frac{1}{2}\right)^2-4.\left(-\frac{1}{2}\right)-5\)
\(h\left(-\frac{1}{2}\right)=\frac{1}{4}-\left(-2\right)-5\)
\(h\left(-\frac{1}{2}\right)=-\frac{11}{4}\)
\(\Rightarrow h\left(x\right)=-\frac{11}{4}\)
\(f\left(-1\right)=5\left(-1\right)^3-7\left(-1\right)^2+\left(-1\right)+7+4\left(-1\right)^5\)
\(f\left(-1\right)=-5-7-1+7-4\)
\(f\left(-1\right)=-10\)
\(g\left(0\right)=4.0^5-3.0^3-7.0^2+2.0+5\)
\(g\left(0\right)=0-0-0+0+5\)
\(g\left(0\right)=5\)
\(h\left(-\frac{1}{2}\right)=\left(-\frac{1}{2}\right)^2-4\left(-\frac{1}{2}\right)-5\)
\(h\left(-\frac{1}{2}\right)=\frac{1}{4}-\left(-2\right)-5\)
\(h\left(-\frac{1}{2}\right)=\frac{1}{4}+2-5\)
\(h\left(-\frac{1}{2}\right)=-\frac{11}{4}\)
Ta có: \(F\left(x\right)+G\left(x\right)-H\left(x\right)=0\)
\(\Leftrightarrow4x^2+3x-2+3x^2-2x+5-5x^2+2x-3=0\\ \Leftrightarrow2x^2+3x=0\\ \Rightarrow x\left(2x+3\right)=0\\ \Rightarrow x=0;x=\dfrac{-3}{2}\)
Vậy tìm được x thỏa mãn là: \(x=0;x=\dfrac{-3}{2}\)
a) Thu gọn, sắp xếp các đa thức theo lũy thừa tăng của biến
= -9 - 2x2 + 3x3 - 6x5 - 3x7
b) Tính -9 - 2x2 + 3x3 - 6x5 - 3x7 ) + (-12 + 3x3 + x4 + x5 - x6 - 6x7 - 5x8 ) - (2x - 3x2 + 4x3 +4x5 -4x6 - 10x7)
= - 9 - 2x2 + 3x3 - 6x5 - 3x7 -12 + 3x3 + x4 + x5 - x6 - 6x7 - 5x8 - 2x + 3x2 - 4x3 - 4x5 + 4x6 + 10x7
= -21 - 2x + x2 + 2x3 + x4 - 9x5 + 3x6 + x7 - 5x8
a) A(x) = f(x) + g(x) = ( 2x^3 + 3x - 4x^3 + 1/2 - 5x^4 ) + ( 3x^4 + 0,2 - 7x^2 + 5x^3 - 9x )
= 2x^3 + 3x - 4x^3 + 1/2 - 5x^4 + 3x^4 + 0,2 - 7x^2 + 5x^3 - 9x
= ( 2x^3 - 4x^3 + 5x^3 ) + ( 3x - 9x ) + ( 1/2 + 0,2 ) + ( -5x^4 + 3x^4 ) - 7x^2
= 3x^3 - 6x + 0,7 - 2x^4 - 7x^2
B(x) = f(x) - g(x) = ( 2x^3 + 3x - 4x^3 + 1/2 - 5x^4 ) - ( 3x^4 + 0,2 - 7x^2 + 5x^3 - 9x )
= 2x^3 + 3x - 4x^3 + 1/2 - 5x^4 - 3x^4 - 0,2 + 7x^2 - 5x^3 + 9x
= ( 2x^3 - 4x^3 - 5x^3 ) + ( 3x + 9x ) + ( 1/2 - 0,2 ) + ( -5x^4 - 3x^4 ) + 7x^2
= -7x^3 + 12x + 0,3 -8x^4 + 7x^2
f(x)+g(x)=12x4-11x3+2x2-\(\frac{1}{4}\)x-\(\frac{1}{4}\)
Con f(x)-g(x) thi tru 2 da thuc tren cho nhau
a: \(f\left(x\right)=x^5-3x^4+2x^3-x^2-4x+1\)
\(g\left(x\right)=x^4-5x^3+2x-1\)
\(f\left(x\right)+g\left(x\right)=x^5-2x^4-3x^3-x^2-2x\)
b: \(A\left(x\right)=f\left(x\right)+g\left(x\right)=x^5-2x^4-2x^3-x^2-2x\)
\(A\left(0\right)=0^5-2\cdot0^4-2\cdot0^3-0^2-2\cdot0=0\)
=>x=0 là nghiệm của A(x)