Quadratics and exponents

Quadratics bring in x squared, and with it a new kind of answer: often two solutions instead of one. Before factoring makes sense, you need the exponent rules solid, because most exponent mistakes come from multiplying powers when they should be added, or adding bases that should stay put. This topic starts there. Then it moves to factoring a quadratic into two brackets, where the key is finding two numbers that multiply to the constant and add to the middle coefficient, with the signs handled carefully. Finally, you use the zero-product rule: if two brackets multiply to zero, one of them must be zero, so each bracket gives its own solution. The most common slip at that stage is trying to use the rule before the equation equals zero. Go through the pages in order, and check each solution by substituting it into the original equation. Both values should work, and a quick check catches a sign error before a test does.