Integrated Math 2 / Unit 4: Solving Quadratic Equations
4.1 Solving by Factoring
Notes
A quadratic equation can be written $ax^2 + bx + c = 0$. If it factors, use the zero product property: if $AB = 0$ then $A = 0$ or $B = 0$.
- Move everything to one side so the other side is 0.
- Example: $x^2 - 5x + 6 = 0 \Rightarrow (x - 2)(x - 3) = 0 \Rightarrow x = 2$ or $x = 3$.
- Never divide both sides by $x$, because you lose the solution $x = 0$. Factor instead.
- Check each solution in the original equation.
Practice
Solve $x^2 - x - 12 = 0$.
$(x - 4)(x + 3) = 0$.
Solve $x^2 = 7x$.
Write $x^2 - 7x = 0$, so $x(x - 7) = 0$. Dividing by $x$ would lose the solution $x = 0$.
Solve $2x^2 + 5x - 3 = 0$.
$(2x - 1)(x + 3) = 0$, so $\displaystyle x = \frac{1}{2}$ or $x = -3$.
Ready for more? Take the Unit 4 test.