Question

If (x + 1)(x - 3) = 12, then which of the following statements is true? Ox+1=0 orx - 3 = 0 Ox+1= 12 or* - 3 = 12 X-5 - 0 or x + 3 = 0 NEXT QUESTION O ASK FOR HELP

Answer 1

`x-5=0\:or\:x+3=0`

1) If this equation in the factored form is equal to 12, then we can tell this:

`\begin{gathered} (x+1)(x-3)=12 \\ x^2-2x-3=12 \\ x^2-2x-3-12=12-12 \\ x^2-2x-15=0 \\ x=(-\left(-2\right)\pm√(\left(-2\right)^2-4\cdot\:1\cdot\left(-15\right)))/(2) \\ x=(-\left(-2\right)\pm\:8)/(2) \\ x_1=5 \\ x_2=-3 \end{gathered}`

If expanding heose parentheses and solving via quadratic formula yields 5 and -3 we can tell that using the factor zero property, this is equivalent to saying that:

`\begin{gathered} (x+1)(x-3)=12 \\ x-5=0\Rightarrow x=5 \\ x+3=0\Rightarrow x=-3 \end{gathered}`