Algebra 1, Please Help! Zero Product Property

Question

1 Use the Zero Product Property to find the values of x that make the equation true.

(x − 4)(2x + 5) = 0

2 Use your skills in factoring trinomials and the Zero Product Property to solve the equation.

x² + 4x − 21 = 0

Answer 1

If (x - 4)(2x+5) = 0, then either or both of the terms = 0

x - 4 = 0 then x = 4; 2x + 5 = 0, then 2x = -5 and x = -5/2

Factor x² + 4x - 21. Factors of the last term, 21, are: ±1, ±21, ±3, ±7. Which combination multiplies to give the -21? Either -7 x 3, or 7 x -3. Which of those add to give the coefficient of the middle term, 4. It's 7 and -3!

So the factors are (x + 7)(x - 3). You can check it by using the FOIL method to multiply it out. You weren't asked to find the zeros, but it would work the same way as the first problem above. Just set the product of the two binomial factors = 0.