# factoring

• Jan 13th 2009, 08:08 PM
21_knip
factoring
can someone tell me how to factor this?
(x-3)(x-1)(x+1)(x+3)+64
thanks.
• Jan 13th 2009, 08:16 PM
mr fantastic
Quote:

Originally Posted by 21_knip
can someone tell me how to factor this?
(x-3)(x-1)(x+1)(x+3)+64
thanks.

If you expand and simplify (and there's an easy way to do this by hand) you get $x^4 - 10x^2 + 73$.

This can be factorised as two irreducible real quadratics factors and four complex linear factors otherwise.
• Jan 13th 2009, 08:20 PM
21_knip
is this the final answer when it is said to factor completely? ur answer, is it still factorable?
• Jan 13th 2009, 08:30 PM
mr fantastic
Quote:

Originally Posted by 21_knip
is this the final answer when it is said to factor completely? ur answer, is it still factorable?

Is the quartic I have given yu to be factorised over real or complex numbers? Start by thinking how to factorise into two irreducible quadratics.
• Jan 13th 2009, 09:24 PM
21_knip
factoring
if i changed 64 to 16 what would be the answer?
(x-3)(x-1)(x+1)(x+3)+16

No. The quartic becomes $x^4 - 10x^2 + 25$ and this has a very simple factorisation (think perfect square) ....