Factoring Trinomials and Zero Product Property 2.5

A trinomial is a polynomial with three terms, typically in the form of $$ax^2 + bx + c$$ .

The Zero Product Property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ .

To factor $$x^2 + 4x - 12$$ , find two numbers that multiply to -12 and add to 4. The factors are (x + 6)(x - 2).

The solutions are $$x = -6$$ or $$x = 2$$ .

To factor $$x^2 - 8x + 15$$ , find two numbers that multiply to 15 and add to -8. The factors are (x - 3)(x - 5).

The solutions are $$x = 3$$ or $$x = 5$$ .

To factor $$x^2 - 9x + 20$$ , find two numbers that multiply to 20 and add to -9. The factors are (x - 4)(x - 5).

The solutions are $$x = 4$$ or $$x = 5$$ .

To factor $$x^2 - 7x + 10$$ , find two numbers that multiply to 10 and add to -7. The factors are (x - 2)(x - 5).

The solutions are $$x = 2$$ or $$x = 5$$ .