find linear factors of this quartic expression

**AlexTweed** · February 7th 2009, 09:15 AM

$f(x)=x^4-7x^3+9x^2+7x-10$
$f(1)=1^4-7*1^3+9*1^2+7*1-10=0$
$x-1$ is a factor, using long devision I have;
$f(x)=x^4-7x^3+9x^2+7x-10=(x-1)(x^3-6x^2+3x+10)=(x-1)g(x)$
$g(2)=2^3-^*2^2+3*2+10=0$
so $x-2$ is a factor, using long devision again I get;
$f(x)=x^4-7x^3+9x^2+7x-10=(x-1)(x-2)(x^2+4x+11+(32/x-2))$
and now I'm stuck, please help

**galactus** · February 7th 2009, 10:01 AM

You have two of them correctly. Now, since two of them can be factored out, you have a quadratic remaining which should be easier.

$\frac{x^{4}-7x^{3}+9x^{2}+7x-10}{(x-2)(x-1)}=x^{2}-4x-5$

You can factor that I am sure.

**AlexTweed** · February 7th 2009, 11:48 AM

Thanks but I'm not sure how you have factored them out? Sorry

**AlexTweed** · February 7th 2009, 12:09 PM

No its ok, you just divide the quartic by x-2 then divide the result buy x-1 to get that quadratic. Dont really know why but that works.

Thread: find linear factors of this quartic expression

LinkBack

Thread Tools

Display

find linear factors of this quartic expression

Similar Math Help Forum Discussions

Cubic Polynomial and Linear Factors

Nonrepeated Linear Factors

product of linear factors

Finding Linear Factors Over C

Linear factors of polynomial

Search Tags