Quadratic equations, patterns and pleasure

One nice thing about helping my children with their homework is that you can re-learn things, or learn new things.

Last night I was helping Sophie with maths, and a couple of the problems required quadratic equations to be factorised. I could do them 'by eye', just seeing them made me guess the solution, and after doing a couple, I noticed a pattern. I have no idea if this pattern is how solving is taught.

If the factors are (x+a), (x+b) [or change either or both + signs to -, it doesn't matter], then expanding these out gives x^2 + (a+b)x + ab. So, if presented with the problem of factorising x^2+cx+d, start by working out the factors of d, and then see which if any of the factors sum to c.

One example we had last night was x^2+13x+30. The factors of 30 include 5+6, 2+15, 3+10, the last of which sum to 13. So here, the solution is (x+3)(x+10).

Simple, but neat.

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