Math CentralQuandaries & Queries


Question from danyelle, a student:


factoring i dont understand it at all


You are trying to find polynomials that multiply to

81x2 + 36x + 4

As the only polynomials with degree lower than a quadratic are linear, the factors must be linear. So you are looking for

Ax + B and Cx + D

such that

(Ax + B)(Cx + D)
= AC x2 + (BC+AD)x + BD
= 81x2 + 36x + 4

So AC = 81, BD =4, and AD+BC = 36.

Try guessing what A and C (and B and D) might be - in this case there is one very easy solution. In general you must use "completing the square" or the quadratic formula when A,B,C,D are not integers.

Factoring higher degree polynomials is not easy unless you can spot a pattern. In particular, there is no elementary formula to factor polynomials of degree five or higher.

Good Hunting!

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