Solve by factoring

Question

Solve by factoring 

a)1/4m²+2m-5=0

b)0=6z²-21z+9

Answer 1

Part a)

 

(1/4)m² + 2m - 5 = 0

 

 

Multiply both sides of equation by 4 to get rid of any denominators.

 

m² + 8m - 20 = 0

 

 

Factor using FOIL method.

 

(m + 10)(m  - 2) = 0

 

 

Set the factors equal to zero.

 

m + 10 = 0         and         m - 2 = 0

 

m = -10      and      m = 2

 

We have two equations.

 

 

Part b)

 

0 = 6z² - 21z + 9

 

 

Factor using FOIL.

 

0 = (3z - 9)(2z - 1)

0 = 3(z - 3)(2z - 1)

 

 

Set the factors equal to zero.

 

z - 3 = 0            and           2z - 1 = 0

 

   z = 3                and            z = 1/2

 

We have two solutions.