Given polynomial $f (x) = x^{3} - 2 x^{2} - 40 x - 64$ $f(x)=x^3-2x^2-40x-64$ and a factor $x - 8$ $x-8$ how do you find all other factors?

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Given polynomial $f (x) = x^{3} - 2 x^{2} - 40 x - 64$ $f(x)=x^3-2x^2-40x-64$ and a factor $x - 8$ $x-8$ how do you find all other factors?

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Answer 1 · 2017-02-23T08:33:48

The other factors are $(x + 2)$ $(x+2)$ and $(x + 4)$ $(x+4)$

Explanation:

We perform a synthetic division

$a a a a$ $color(white)(aaaa)$ $8$ $8$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 2$ $-2$ $a a a a a$ $color(white)(aaaaa)$ $- 40$ $-40$ $a a a a a a$ $color(white)(aaaaaa)$ $- 64$ $-64$

$a a a a a a$ $color(white)(aaaaaa)$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $8$ $8$ $a a a a a a$ $color(white)(aaaaaa)$ $48$ $48$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $64$ $64$

$a a a a a a a a a a$ $color(white)(aaaaaaaaaa)$ ------------------------------------------------------------

$a a a a$ $color(white)(aaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $1$ $1$ $a a a a a$ $color(white)(aaaaa)$ $6$ $6$ $a a a a a a a$ $color(white)(aaaaaaa)$ $8$ $8$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $0$ $color(red)(0)$

The remainder is $= 0$ $=0$

The quotient is $= x^{2} + 6 x + 8$ $=x^2+6x+8$

This is factorised as

$x^{2} + 6 x + 8 = (x + 2) (x + 4)$ $x^2+6x+8=(x+2)(x+4)$

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Given polynomial $f (x) = x^{3} - 2 x^{2} - 40 x - 64$ $f(x)=x^3-2x^2-40x-64$ and a factor $x - 8$ $x-8$ how do you find all other factors?

1 Answer

Explanation:

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Given polynomial f(x)=x^3-2x^2-40x-64f(x)=x3−2x2−40x−64f(x)=x^3-2x^2-40x-64 and a factor x-8x−8x-8 how do you find all other factors?

1 Answer

Explanation:

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Impact of this question

Given polynomial $f (x) = x^{3} - 2 x^{2} - 40 x - 64$ $f(x)=x^3-2x^2-40x-64$ and a factor $x - 8$ $x-8$ how do you find all other factors?