Math CentralQuandaries & Queries


Question from Adrienne, a student:

a field has an area of (x^2+x-6) square metres. State expressions for its length and width.

Hi Adrienne,

I think what you are being asked here is to factor x2 + x - 6. I am going to illustrate what I would do with by factoring example x2 - 3x - 10.

The number 10 factors as 1 × 10 or 2 × 5 and hence x2 - 3x - 10, if it factors at all, will factor as

(x ± a)(x ± b)

where a and b are either 1 and 10 or 2 and 5. Since the constant term is -10 I know that the signs must differ. Try the possible combinations and each time expand (x ± a)(x ± b) to see if you get x2 - 3x - 10.

I hope this helps,

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