Using the procedure for factoring attached to the test, factor this equation, then check yourself: y = -5x² - 8x + 4

Question

(x - 10)(x + 2)

(-5x - 2)(x - 2)

(5x - 2)(x + 2)

(x + 10)(x - 2)

(-5x + 2)(x + 2)

Answer 1

Factor the equation using FOIL.

 

In the first step, your factored form should be

 

(-5x + a)(x + b)

 

This is because the first terms when multiplied together must be -5x².

 

 

Next, we find values of a and b , so that the product of a and b is 4.  Also, the sum of the inner and outer terms must be -8x.

 

 

The only values of a and b that we can have are ±1, ±2, and ±4.

 

By experimenting, a=2 and b=2.  So we have

 

y = (-5x + 2)(x + 2)

 

To check this answer, use FOIL to expand.  You should get back the equation in standard form that we started with.