If $x+4$ is a factor of the polynomial $x^3-x^2-14x+24$. Find the other factors.
Given: $(x + 4)$ is a factor of $x^3-x^2-14x+24$.
To do: Find other factors, we have to divide by $(x + 4)$.
Solution:
$x^3 - x^2 - 14x + 24$
⇒ $x^2 + 4x^2 - 5x^2 - 20x + 6x + 24$
⇒ $x^2(x + 4) - 5x(x + 4) + 6(x + 4) $
⇒ $(x + 4)(x^2 - 5x + 6)$
We get quotient $(x^2 - 5x + 6)$. This is the product of other two factors.
Now we have to factories $(x^2 - 5x + 6)$.
$x^2 - 5x + 6$
⇒ $x^2 - 3x - 2x + 6$
⇒ $x(x - 3) - 2(x - 3)$
⇒ $(x - 2)(x - 3)$
The other factors are : $(x - 2)$ and $(x - 3)$.
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