Question

Cho F(x)=5x\(^2\)-1+3x+x\(^2\)-5x\(^3\) và G(x)=2-3x\(^3\)+6x\(^2\)+5x-2x\(^3\)-x

a)Thu gọn đa thức F(x),G(x) và tính F(x)-G(x).

b)Tìm đa thức N(x),biết rằng N(x)+F(x)= -G(x)

Answer 1

a) \(...F\left(x\right)=-5x^3+6x^2+3x-1\)

\(...G\left(x\right)=-5x^3+6x^2+4x+2\)

\(\Rightarrow F\left(x\right)-G\left(x\right)=-x-3\)

b) \(N\left(x\right)+F\left(x\right)=-G\left(x\right)\)

\(\Rightarrow N\left(x\right)=-F\left(x\right)-G\left(x\right)\)

\(\Rightarrow N\left(x\right)=-\left[F\left(x\right)+G\left(x\right)\right]\)

\(\Rightarrow N\left(x\right)=-\left(-10x^3+12x^2+7x+1\right)=10x^3-12x^2-7x-1\)

Answer 2

a, F(x)= 5x² -1 +3x + x² - 5x³

    F(x)= -5x³ + (5x² + x²) + 3x - 1

    F(x)= -5x³ + 6x² + 3x - 1

G(x)= 2 - 3x³ + 6x² + 5x - 2x³ - x

G(x)= (-3x³ - 2x³) + 6x² + (5x - x) + 2

G(x)= -5x³ + 6x² + 4x + 2

F(x)-G(x)= -5x³ + 6x² + 3x - 1 - (-5x³ + 6x² + 4x + 2)

               = -5x³ + 6x² + 3x - 1 + 5x³ - 6x² - 4x - 2

               = (−5x³ + 5x)+(6x² − 6x)+(3x − 4x)+(−1 − 2)

               = -x - 3

b, Ta có: N(x)+F(x)= -G(x) ⇒ N(x) = −G(x) − F(x)

N(x) = −(−5x³ + 6x + 4x + 2)−(−5x³ + 6x + 3x − 1)

        = 5x³ − 6x − 4x − 2 + 5x³ − 6x − 3x + 1

        =(5x³ + 5x)+(−6x² - 6x)+(−4x − 3x)+(−2 + 1)

        =10x − 12x − 7x − 1