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# Use factoring and the zero product property to solve the following: z(z+1)(z+3)=0

anya4one | Student, Undergraduate | Honors

Posted July 16, 2013 at 4:26 PM via web

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Use factoring and the zero product property to solve the following:

z(z+1)(z+3)=0

Tagged with algebra, factoring, math

### 2 Answers |

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 16, 2013 at 4:37 PM (Answer #1)

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`z(z+1)(z+3) = 0`

The above function is already in the factorized form with z,(z+1) and (z+3) as factors.

`f(x) = z(z+1)(z+3)`

Using zero product property to f(x) = 0 we need either;

`z = 0`

`(z+1) = 0`

`(z+3) = 0`

So the values of z that satisfy f(x) = 0 are;

z = 0

z = -1

z = -3

Sources:

mtester | eNoter

Posted July 17, 2013 at 2:06 PM (Answer #2)

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z(z+1)(z+3)=0

Since the product of the three factors, z, (z+1) and (z+3), equals zero one of the factors must equal zero according to the zero product property. Therefore either

z=0,z+1=0, or z+3=0

solve each equation for z and your answer is

z=0

z+1-1 =0-1 so z=-1

z + 3-3 = 0-3 so z = -3

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