Question

Dane są wielomiany p(x) = 3x+2 i q(x) = x^2 - 3x. Wykonaj wskazane działania i uporządkuj otrzymany wielomian.
a) (p(x) + q (x))^2
b) (p(x)-q(x))^2

Answer 1

P(x) = 3 x + 2

Q(x) = x^2 - 3 x

a)

Mamy        P(x) + Q(x) = 3 x + 2 + x^2 - 3x = x^2 + 2

zatem

( P(x) + Q(x))^2 = ( x^2 + 2)^2 = x^4 + 4 x^2 + 4

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b)

Mamy      P(x) - Q(x) = 3x + 2 - ( x^2 - 3x)  = 6x + 2 - x^2

zatem

( P(x) - Q(x))^2 = [ 6x + 2 - x^2)^2 = (6x + 2)^2  - 2*(6x +2)*x^2 + x^4 =

= 36 x^2 + 24 x + 4  - 12 x^3 - 4 x^2 + x^4 =  x^4 - 12 x^3 + 32 x^2 + 24 x + 4

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