Question

Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12.

Answer 1

Answer: Sol={-6,1}

Explanation:

1) we are searching value of x in R

`(x+2)(x+3)=12\\x^2+2x+3x+6-12=0\\x^2+5x-6=0\\\\x^2-x+6x-6=0\\\\x(x-1)+6(x-1)=0\\\\(x-1)(x+6)=0\\\\x=1\ or\ x=-6\\Sol=\{-6,1\}\\`

2) we are searching value of x in Z.

12=1*12 =(-1)*(-12)

12=2*6=(-2)*(-6)

12=3*4=(-3)*(-4)

`\begin{array}x=&x+2=&x+3=&(x+2)(x+3)=&is\ solution\\---&---&---&---&---\\1&3&4&12&True\\2&4&5&20&False\\3&5&6&30&False\\4&6&7&42&False\\6&8&9&72&False\\12&14&15&210&False\\---&---&---&---&---\\-1&1&0&0&False\\-2&0&1&0&False\\-3&1&2&2&False\\-4&2&3&6&False\\-6&-4&-3&12&True\\-12&-10&-9&90&False\\---&---&---&---&---\\\end{array}\\\\\\\boxed{Sol=\{-6,1\}}`

Answer 2

Solution

x=1

x=−6

Explanation:

x(+3)+2(x+3)=12