Question

Tính \(f\left(x\right)+g\left(x\right)-h\left(x\right)\) biết :

\(f\left(x\right)=x^5-4x^3+x^2-2x+1\)

\(g\left(x\right)=x^5-2x^4+x^2-5x+3\)

\(h\left(x\right)=x^4-3x^2+2x-5\)

Answer 1

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)=

Answer 2

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