If 1 and −2 are zeroes of the polynomial x² + ax + b, find the values of a and b.

1. 1 · Write what is given and what is to be found. p(x) = x² + ax + b has zeroes 1 and −2. To find: a and b.
2. 2 · Write the rule. If k is a zero of p(x), then p(k) = 0.
3. 3 · Put x = 1. 1 + a + b = 0, so a + b = −1 ... (1)
4. 4 · Put x = −2. 4 − 2a + b = 0, so −2a + b = −4 ... (2)
5. 5 · Solve the two equations. Subtract (2) from (1): 3a = 3, so a = 1. Then from (1), b = −1 − 1 = −2.
6. 6 · Check and box the answer. p(x) = x² + x − 2. p(1) = 1 + 1 − 2 = 0 and p(−2) = 4 − 2 − 2 = 0. Therefore a = 1 and b = −2.

Scoring tip: Number your two equations. Then you can say 'subtract (2) from (1)' in one clear line.