Question

Dividindo o polinômio P(×)=׳-5ײ+8 pelo polinômio H(×)=×-3 encontraremos o quociente:


A) x²-5×+2
B) x³-3ײ+2×11
C) x²+2×+1
D) x³-5ײ+×-5
E) x²-2×-6
alguém poderia me ajudar .​

Answer 1

Resposta:

q(x) = x² - 2x - 6

r = -10

x³ - 5x² + 8 = p(x).q(x) + r

\begin{gathered} x^{3}-5x^{2} +8=p(x)(x^{2}-2x-6)-10 \\ x^{3}-5x^{2}+8+10=p(x)( x^{2} -2x-6) \\ x^{3}-5 x^{2} +18= p(x)(x^{2} -2x-6) \\ \\ p(x)= \frac{x^{3}-5 x^{2} +18}{x^{2} -2x-6} \\ \\ p(x)= \frac{(x-3)(x^{2} -2x-6)}{(x^{2} -2x-6)} \\ \\ p(x) = x-3\end{gathered}

x

3

−5x

2

+8=p(x)(x

2

−2x−6)−10

x

3

−5x

2

+8+10=p(x)(x

2

−2x−6)

x

3

−5x

2

+18=p(x)(x

2

−2x−6)

p(x)=

x

2

−2x−6

x

3

−5x

2

+1

p(x)=xx3

Explicação passo-a-passo:

q(x) = x² - 2x - 6

r = -10

x³ - 5x² + 8 = p(x).q(x) + r

\begin{gathered} x^{3}-5x^{2} +8=p(x)(x^{2}-2x-6)-10 \\ x^{3}-5x^{2}+8+10=p(x)( x^{2} -2x-6) \\ x^{3}-5 x^{2} +18= p(x)(x^{2} -2x-6) \\ \\ p(x)= \frac{x^{3}-5 x^{2} +18}{x^{2} -2x-6} \\ \\ p(x)= \frac{(x-3)(x^{2} -2x-6)}{(x^{2} -2x-6)} \\ \\ p(x) = x-3\end{gathered}

x

3

−5x

2

+8=p(x)(x

2

−2x−6)−10

x

3

−5x

2

+8+10=p(x)(x

2

−2x−6)

x

3

−5x

2

+18=p(x)(x

2

−2x−6)

p(x)=

x

2

−2x−6

x

3

−5x

2

+18

p(x)=

(x

2

−2x−6)

(x−3)(x

2

−2x−6)

p(x)=x−3