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If the coefficients of a polynomial add to zero, then (x-1) is a factor. For example, let's try and factorise f(x) = 2x^3 + 9x^2 + 4x - 15 What happens if we
by SandB0x 16y ago
If the coefficients of a polynomial add to zero, then (x-1) is a factor.
For example, let's try and factorise f(x) = 2x^3 + 9x^2 + 4x - 15
What happens if we set x = 1? Then f(1) = 2 + 9 + 4 - 15 = 0, so (x-1) must be a factor.
It's much easier to get f(x) = (x - 1)(2x^2 + 11x + 15) = (x - 1)(x + 3)(2x + 5) if you know one of the factors in advance. This was useful at school, at least. Not so much now.
* See http://en.wikipedia.org/wiki/Polynomial_remainder_theorem http://en.wikipedia.org/wiki/Polynomial_remainder_theorem
- deleted 16y ago[deleted]
- scorpion032 16y agoAs a corollary, on the same lines of thinking, If the co-efficients of the odd powers and the even powers are equal, then (x+1) is a factor.
- runjake 16y agoEither somebody picked up the telephone while you were online typing this out, or I need to take more math classes.
- jtheory 16y agoSurely one of you hackers can offer us a practical application for any nifty math tricks on display in these comments. I'm, ah, coming up blank on this one for now.