solving by factoring

Question

what two numbers multiply to give you-5 but add to give you-4

Answer 1

Well ...the only numbers that multiply to make -5 are 1(-5) or -1(5).

1 + -5 = -4

-1 + 5 = 4

So it's the first pair 1 and -5!

Answer 2

My favorite (and I think the easiest) way to do this is by listing the factors of the product, which in this case is -5:

5*-1= -5

-5*1=-5

Luckily these are the only two "factors" that multiply to get -5. Now figure out which of these options adds up to -4. Your first option is 5 and -1 and your second option is -5 and 1. 5-1=4, but -5+1=-4, so your answer is -5 and 1!

Answer 3

Can you factor and solve for a and b?

Answer 4

Since the product is negative one of the numbers must be positive and the other negative. The only integers that multiply to give a result of - 5 are: -1 times 5 OR 1 times - 5. The first combination results in a sum of +4. The 2nd combination results in 1 + (-5) = -4, so that is the combination that answers the question.

Likely you are trying to factor the following trinomial:

x² - 4x - 5 which does factor into the product of two binomials:

(x - 5)(x + 1)

Factoring is one technique that can be used to solve a quadratic equation like this:

x² - 4x - 5 = 0

(x - 5) (x + 1) = 0

x - 5 = 0 OR x + 1 = 0 : this is called the zero product property

x = 5 OR x = -1

Check:

5² - 4(5) - 5

25 - 20 - 5

0

(-1)² -4(-1) - 5

1 + 4 - 5

0

Answer 5

For a small number like this you can consider finding the factors of -5 which are -1 , 5 and 1 , -5. You can them combine (add) each pair (trial & error) to see which gives you a sum of -4. -1 + 5 = 4. 1 +(-5) = -4. so you answer is 1 -5.