Question

Fie polinoamele P(X)=2X ⁴-5x³+3x²-6x+Q(x)=-5x⁴+2x³-7x²-11 aflati suma si diferenta polinoamelor S(x)=Q(x) si D(x) =P(x) - Q(x)
precizati gradul polinoamelor S(x) si D(x)

Answer 1

P (X) = 2 X⁴ - 5 X³ + 3 X² - 6 X + Q (X) = -5 X⁴ + 2 X³ - 7 X² - 11
S (X) = Q (X) = ?
D (X) = P (X) - Q (X) = ?

Q (X) = -5 X⁴ + 2 X³ - 7 X² - 11 - (2 X⁴ - 5 X³ + 3 X² - 6 X) =
= -5 X⁴ + 2 X³ - 7 X² - 11 - 2 X⁴ + 5 X³ - 3 X² + 6 X =
= -7 X⁴ + 7 X³ - 10 X² + 6 X - 11.

Deci S (X) = Q (X) = -7 X⁴ + 7 X³ - 10 X² + 6 X - 11.

D (X) = P (X) - Q (X) = -5 X⁴ + 2 X³ - 7 X² - 11 - (-7 X⁴ + 7 X³ - 10 X² + 6 X - 11)
D (X) = -5 X⁴ + 2 X³ - 7 X² - 11 + 7 X⁴ - 7 X³ + 10 X² - 6 X + 11 =
= 2 X⁴ - 5 X³ + 3 X² - 6 X.

Deci D (X) = P (X) - Q (X) = 2 X⁴ - 5 X³ + 3 X² - 6 X.

grad S (X) = 4 , grad D (X) = 4.