Dane Sa wielomiany

[sloma]

Dane sa wielomiany \(\displaystyle{ W(x) = 5x ^{3} +2x ^{2} -3, p(x) = x-1}\) OBLICZ:

A) \(\displaystyle{ w(x)-3 \cdot p(x) =}\)
b) \(\displaystyle{ w(x) \cdot p(x) =}\)
c) \(\displaystyle{ (p(x)) ^{2} \cdot x - w(x) =}\)

[emelcia]

Dane sa wielomiany \(\displaystyle{ w(x) = 5x ^{3} +2x ^{2} -3, p(x) = x-1}\) OBLICZ:

A) \(\displaystyle{ w(x)-3 \cdot p(x) =}\)
b) \(\displaystyle{ w(x) \cdot p(x) =}\)
c) \(\displaystyle{ (p(x)) ^{2} \cdot x - w(x) =}\)

\(\displaystyle{ w(x)-3 \cdot p(x) = 5x ^{3} +2x ^{2} -3 -3(x-1) = 5x ^{3} +2x ^{2} -3 -3x +3 = 5x ^{3} +2x ^{2} -3x}\)

\(\displaystyle{ w(x) \cdot p(x) = (5x ^{3} +2x ^{2} -3) \cdot (x-1) = 5x ^{4} +2x ^{3} -3x -5x ^{3} -2x ^{2} + 3 = 5x ^{4} - 3x ^{3} - 2x ^{2} - 3x +3}\)

\(\displaystyle{ (p(x)) ^{2} \cdot x - w(x) = (x-1) ^{2} \cdot x - (5x ^{3} +2x ^{2} -3) = x(x^{2} - 2x + 1) - (5x ^{3} +2x ^{2} -3) = x ^{3} - 2x ^{2} + x - 5x ^{3} - 2x ^{2} + 3 = -4x^{3} - 4x ^{2} + x + 3}\)

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