use the zero factor property to solve

Question

x^2+8x+15=0

 

 

 

 

3x^2+8x-3=0

Answer 1

x²+8x+15=0

 

(x+m)(x+n) = 0

 

We want:

m+n = 8

m*n = 15

 

Factors of 15 = 15*1, 5*3  Let's try 5 and 3

 

5+3=8

5*3=15

 

5 and 3 work, so m=3, n=5

 

(x+3)(x+5)=0

 

x= -3 and -5

 

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3x^2+8x-3=0

 

This is a bit more complicated.  The factors will be:

 

(3x+m)(x+n)  If you multiply them out you get

 

3x² + (3n+m)x + mn = 0

 

So you need an m and n such that:

 

3n+m = 8

mn = -3

 

Factors of mn = -3 = -3*1, -1*3

 

Try n=-3 and m=1

 

3n+m = 3(-3)+1 = -9+1 = -8    We need +8 not -8 so this doesn't work

 

Try n=3, m=-1

 

3n+m = 3(3)+(-1) = 9 = 1 = 8  This works so

 

m=-1, n=3

 

Factors are:

 

(3x-1)(x+3)

 

x = 1/3, -3

 

Answer 2

I am assuming that those are both different equations and are two different problems. Looking for the zeros is just basically knowing what the x's are. So in the first equation,

 

x^2+8x+15 = 0 ; you are just looking for the factors of the equation. So it would look like

 

x^2+8x+15=0

(x-"  ") (x-"  ")     "  " represents the numbers that would be present. Remember that the minus sign can be                           a plus sign as well. It just has to make up to be what the equation should be when                                     expanded.

 

So you are basically looking for numbers multiplied to equal 15 and add up to be 8, which both are positive numbers.

 

So you would end up with (x+5)(x+3) to equal x^2+8x+15, therefore, x=-5,-3.

 

You would simply do the same for the 2nd equation.