Question

Cho P(x)= \(2x^4-3x^2+x-\dfrac{2}{3}\)   Q(x)= \(x^4-x^3+x^2+\dfrac{5}{3}\)

a, Tính P(x) + Q(x)

b, Tính P(x) - Q(x)

Giúp mik!!!

Answer 1

\(P\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}\)

\(Q\left(x\right)=x^4-x^3+x^2+\dfrac{5}{3}\)

a) \(P\left(x\right)+Q\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}+x^4-x^3+x^2+\dfrac{5}{3}\)

\(\Rightarrow P\left(x\right)+Q\left(x\right)=3x^4-x^3-2x^2+x-\dfrac{2}{3}+\dfrac{5}{3}\)

\(\Rightarrow P\left(x\right)+Q\left(x\right)=3x^4-x^3-2x^2+x+1\)

b) \(P\left(x\right)-Q\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}-\left(x^4-x^3+x^2+\dfrac{5}{3}\right)\)

\(\Rightarrow P\left(x\right)-Q\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}-x^4+x^3-x^2-\dfrac{5}{3}\)

\(\Rightarrow P\left(x\right)-Q\left(x\right)=x^4+x^3-4x^2+x-\dfrac{2}{3}-\dfrac{5}{3}\)

\(\Rightarrow P\left(x\right)-Q\left(x\right)=x^4+x^3-4x^2+x-\dfrac{7}{3}\)

Answer 2

a) P(x) + Q(x) = (2x⁴ - 3x² + x - 2/3) + (x⁴ - x³ + x² + 5/3)

= 2x⁴ - 3x² + x - 2/3 + x⁴ - x³ + x² + 5/3

= (2x⁴ + x⁴) - x³ + (-3x² + x²) + x + (-2/3 + 5/3)

= 3x⁴ - x³ - 2x² + x + 1

b) P(x) - Q(x) = (2x⁴ - 3x² + x - 2/3) - (x⁴ - x³ + x² + 5/3)

= 2x⁴ - 3x² + x - 2/3 - x⁴ + x³ - x² - 5/3

= (2x⁴ - x⁴) + x³ + (-3x² - x²) + x + (-2/3 - 5/3)

= x⁴ + x³ - 4x² + x - 7/3