If x^2 + px + 1 is a factor of ax^3 + bx + c, | vedclass

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(B) Since $x^2 + px + 1$ is a factor of $ax^3 + bx + c$,we perform polynomial division:$ax^3 + bx + c = (x^2 + px + 1)(ax - ap) + (b - a + ap^2)x + (a

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$a^2 - c^2 = ab$

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(B) Since $x^2 + px + 1$ is a factor of $ax^3 + bx + c$,we perform polynomial division:$ax^3 + bx + c = (x^2 + px + 1)(ax - ap) + (b - a + ap^2)x + (ap + c)$For $x^2 + px + 1$ to be a factor,the remainder must be zero:$1) \ ap + c = 0 \Rightarrow p = -\frac{c}{a} \dots (i)$$2) \ b - a + ap^2 = 0$Substituting $(i)$ into the second equation:$b - a + a(-\frac{c}{a})^2 = 0$$b - a + a(\frac{c^2}{a^2}) = 0$$b - a + \frac{c^2}{a} = 0$Multiplying by $a$:$ab - a^2 + c^2 = 0$$a^2 - c^2 = ab$

If $x^2 + px + 1$ is a factor of $ax^3 + bx + c$,then

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