What are the possible integral zeros of $P (x) = x^{3} + 3 x^{2} - 6 x - 8$ $P(x)=x^3+3x^2-6x-8$ ?

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What are the possible integral zeros of $P (x) = x^{3} + 3 x^{2} - 6 x - 8$ $P(x)=x^3+3x^2-6x-8$ ?

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Answer 1 · 2018-01-05T08:50:04

$x = - 4, x = - 1 and x = 2$ $x=-4,x=-1" and "x=2$

Explanation:

$note that$ $"note that "$

$f (2) = 8 + 12 - 12 - 8 = 0$ $f(2)=8+12-12-8=0$

$\Rightarrow (x - 2) is a factor$ $rArr(x-2)" is a factor"$

$x^{2} (x - 2) + 2 x^{2} + 3 x^{2} - 6 x - 8$ $color(red)(x^2)(x-2)color(magenta)(+2x^2)+3x^2-6x-8$

$= x^{2} (x - 2) + 5 x (x - 2) + 10 x - 6 x - 8$ $=color(red)(x^2)(x-2)color(red)(+5x)(x-2)color(magenta)(+10x)-6x-8$

$=color(red)(x^2)(x-2)color(red)(+5x)(x-2)color(red)(+4)(x-2)cancel(color(magenta)(+8))cancel(-8)$

$rArrx^3+3x^2-6x-8$

$=(x-2)(x^2+5x+4)$

$=(x-2)(x+1)(x+4)=0$

$rArrx=-4,x=-1" and "x=2larrcolor(blue)"are the zeros"$

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What are the possible integral zeros of $P (x) = x^{3} + 3 x^{2} - 6 x - 8$ $P(x)=x^3+3x^2-6x-8$ ?

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What are the possible integral zeros of P(x)=x^3+3x^2-6x-8P(x)=x3+3x2−6x−8P(x)=x^3+3x^2-6x-8?

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What are the possible integral zeros of $P (x) = x^{3} + 3 x^{2} - 6 x - 8$ $P(x)=x^3+3x^2-6x-8$ ?