Taking the common factor out of brackets
To factor a polynomial means to write it as a product of several polynomials. If all terms of a polynomial share a common factor, we take it out of brackets: ab + ac = a(b + c); this is the distributive law used in reverse. To find the common factor, we take the greatest common divisor of the coefficients and the lowest power of each common letter: 18a³b² + 24a²b³ = 6a²b²(3a + 4b). The common factor can itself be a polynomial: 5(x - y) + a(x - y) = (x - y)(5 + a). Sometimes we use a - b = -(b - a) to obtain identical brackets. We check the result by multiplying out the brackets; the method also makes calculations easier: 37 · 45 + 37 · 55 = 37 · 100 = 3700.
“Common factor hunters”: a card shows a polynomial such as 12m² - 8m. A group finds the common factor and takes it out; the neighbouring group checks by multiplying.