Question

Match the reasons with the statements. GIVEN: x2 + 6x + 2x + 12 = 0 TO PROVE: x = -6 or x = -2 1. x2 + 6x + 2x + 12 = 0 Subtraction property of equality 2. x2 + 8x + 12 = 0 Distributive Postulate 3. (x + 6)(x + 2) = 0 Combining like terms 4. x + 6 = 0 or x + 2 = 0 Zero product postulate 5. x = -6 or x = -2

Answer 1

Given:
`x^2 + 6x + 2x + 12 = 0.`

1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):

`x^2+(6x+2x)+12=0,\\\\x^2+8x+12=0.`

2. Distributive postulate:

`x^2+8x+12=(x+6)(x+2).`

The equation is

`(x+6)(x+2)=0.`

3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):

`x+6=0 \text{ or } x+2=0.`

4. Subtraction property of equality:

a) subtract 6 from the first equation:

`x+6=0\Rightarrow x+6-6=-6, \ x=-6.`

b) subtract 2 from the second equation:

`x+2=0\Rightarrow x+2-2=-2, \ x=-2.`

Answer 2

1. x2 + 6x + 2x + 12 = 0 1. Given

2. x2 + 8x + 12 = 0 2. Combining like terms

3. (x + 6)(x + 2) = 0 3. Distributive Postulate

4. x + 6 = 0 or x + 2 = 0 4. Zero product postulate

5. x = -6 or x = -2 5 Subtraction property of equality