ZERO PRODUCT PROPERTY TO SOLVE THE EQUATION 

Solve each equation by using the zero product property.

Problem 1 :

(n - 5) (n + 3) = 0

Solution :

(n - 5) (n + 3) = 0

By using zero product property,

n - 5 = 0 or n + 3 = 0

n = 5 or n = -3

So, the solution is n = 5 or -3.

Problem 2 :

(x - 3) (x + 1) = 0

Solution :

(x - 3) (x + 1) = 0

By using zero product property,

x - 3 = 0 or x + 1 = 0

x = 3 or x = -1

So, the solution is x = 3 or -1.

Problem 3 :

(a + 3) (a + 8) = 0

Solution :

(a + 3) (a + 8) = 0

By using zero product property,

a + 3 = 0 or a + 8 = 0

a = -3 or a = -8

So, the solution is a = -3 or -8.

Problem 4 :

m(m + 7) = 0

Solution :

m(m + 7) = 0

By using zero product property,

m = 0 or m + 7 = 0

m = 0 or m = -7

So, the solution is m = 0 or -7.

Problem 5 :

(3x - 8) (x - 3) = 0

Solution :

(3x - 8) (x - 3) = 0

By using zero product property,

3x - 8 = 0 or x - 3 = 0

3x = 8 or x = 3

x = 8/3

So, the solution is x = 8/3 or 3.

Problem 6 :

(3p + 1) (8p - 3) = 0

Solution :

(3p + 1) (8p - 3) = 0

By using zero product property,

3p + 1 = 0 or 8p - 3 = 0

3p = -1 or 8p = 3

p = -1/3 or p = 3/8

So, the solution is p = -1/3 or 3/8.

Problem 7 :

(a - 7) (a - 3) = 0

Solution :

(a - 7) (a - 3) = 0

By using zero product property,

a - 7 = 0 or a - 3 = 0

a = 7 or a = 3

So, the solution is a = 7 or 3.

Problem 8 :

(4v + 5) (v + 7) = 0

Solution :

(4v + 5) (v + 7) = 0

By using zero product property,

4v + 5 = 0 or v + 7 = 0

4v = -5 or v = -7

v = -5/4

So, the solution is v = -5/4 or -7.

Problem 9 :

3p(5p - 1) = 0

Solution :

3p(5p - 1) = 0

By using zero product property,

3p = 0 or 5p - 1 = 0

p = 0/3 or 5p = 1

p = 0 or p = 1/5

So, the solution is p = 0 or 1/5.

Problem 10 :

(v + 8)² = 0

Solution :

(v + 8)² = 0

v² + 2(v) (8) + 64 = 0

v² + 16v + 64 = 0

v² + 8v + 8v + 64 = 0

v(v + 8) + 8(v + 8) = 0

(v + 8) (v + 8) = 0

By using zero product property,

v + 8 = 0 or v + 8 = 0

v = -8 or v = -8

So, the solution is v = -8.