Answer:
1. (2x + 4)(x - 3) = 0
2. The solutions to the expression are
-2 and 3.
Explanation:
1. The expression 2x² - 2x - 12 = 0
can be expressed in factor form as follow:
2x² - 2x - 12 = 0
Multiply the first term i.e 2x² and the last term i.e -12 together. We have:
2x² × -12 = -24x²
Next, look for two factors of -24x² such that their sum will result to the 2nd term i.e -2x in the expression above. The two factors are -6x and 4x.
Next, substitute -6x and 4x in place of -2x in the expression above i.e
2x² - 2x - 12 = 0
2x² - 6x + 4x - 12 = 0
Next, we shall factorize
2x(x - 3) + 4(x - 3) = 0
(2x + 4)(x - 3) = 0
2. The solution to expression
(2x + 4)(x - 3) = 0
2x + 4 = 0 or x - 3 = 0
Collect like terms
2x = 0 - 4 or x = 0 + 3
2x = - 4 or x = 3
x = - 4/2 or x = 3
x = - 2 or 3
Therefore, the solutions to the expression are - 2 and 3.