How do you completely factor $x^{3} - x^{2} - 14 x + 25$ $x^3-x^2-14x+25$ given x-3 is one of the factors?

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How do you completely factor $x^{3} - x^{2} - 14 x + 25$ $x^3-x^2-14x+25$ given x-3 is one of the factors?

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Answer 1 · 2016-11-02T03:32:00

$x - 3$ $x-3$ is not a factor.

Explanation:

Factor $x^{3} - x^{2} - 14 x + 25$ $x^3-x^2-14x+25$ given $x - 3$ $x-3$ is a factor.

Use synthetic division.

$3 ∣ 1 a a - 1 a a - 14 a a a 25$ $3|1color(white)(aa)-1color(white)(aa)-14color(white)(aaa)25$
$a a ↓ a a a a 3 a a a a a 6 a - 24$ $color(white)(aa)darrcolor(white)(aaaa)3color(white)(aaaaa)6color(white)(a)-24$
$a a a$ $color(white)(aaa)$ --------------------------------
$a a a 1 a^{22} a a 2 a^{2} a - 8 a a a 1$ $color(white)(aaa)1color(white)(a^22aa)2color(white)(a^2a)-8color(white)(aaa)1$

The remainder is 1 instead of zero, so $x - 3$ $x-3$ is not a factor.

Perhaps the $25$ $25$ was a typo, and should have been a $24$ $24$ .

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How do you completely factor $x^{3} - x^{2} - 14 x + 25$ $x^3-x^2-14x+25$ given x-3 is one of the factors?

1 Answer

Explanation:

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How do you completely factor $x^{3} - x^{2} - 14 x + 25$ $x^3-x^2-14x+25$ given x-3 is one of the factors?