Question

Solve each equation by rewriting it in factored form and using the zero product property. Show each step.

22 + 12x +11
a) (2x + 1)(x + 11) = 0
b) (2x - 1)(x - 11) = 0
c) (x + 1)(x + 11) = 0
d) (x - 1)(x - 11) = 0

Answer 1

To solve each equation by rewriting it in factored form and using the zero product property, factor the quadratic equation and set each factor to zero. The solutions will be the values of x that make each factor equal to zero.

Step-by-step explanation:

To solve each equation by rewriting it in factored form and using the zero product property, we need to factor the quadratic equation. Let's go through each option:

1. (a) (2x + 1)(x + 11) = 0:
   We set each factor to zero and solve for x:
   
   • 2x + 1 = 0 → 2x = -1 → x = -1/2
   • x + 11 = 0 → x = -11
   
   So, the solutions are x = -1/2 and x = -11.
2. (b) (2x - 1)(x - 11) = 0:
   Solving for x, we get x = 1/2 and x = 11.
3. (c) (x + 1)(x + 11) = 0:
   The solutions for this equation are x = -1 and x = -11.
4. (d) (x - 1)(x - 11) = 0:
   We find x = 1 and x = 11 as solutions to this equation.