Algebra 1 / Unit 9: Quadratic Functions and Equations
9.3 Solving Quadratics by Factoring
Notes
The zero product property: if $ab = 0$, then $a = 0$ or $b = 0$. 1. Set the equation equal to 0. 2. Factor. 3. Set each factor equal to 0 and solve. Example: $x^2 - x = 12 \Rightarrow x^2 - x - 12 = 0 \Rightarrow (x - 4)(x + 3) = 0$, so $x = 4$ or $x = -3$. The solutions are the $x$-intercepts of $y = x^2 - x - 12$.
Practice
Solve $(x - 2)(x + 9) = 0$.
Set each factor to 0.
Solve $x^2 + 5x + 6 = 0$.
$(x + 2)(x + 3) = 0$.
Solve $x^2 = 7x$.
$x^2 - 7x = 0 \Rightarrow x(x - 7) = 0$. Don't divide by $x$, or you lose $x = 0$.
Ready for more? Take the Unit 9 test.