Question

"Factor 3x^2+3x-6" "Answer: 3(x-1)(x+2)

Answer 1

Answer:

Step-by-step explanation:

3x²+3x-6

=3(x²+x-2)

=3(x²+2x-x-2)

=3[x(x+2)-1(x+2)]

=3(x+2)(x-1)

Answer 2

Answer:

3(x - 1)(x + 2)

Step-by-step explanation:

Factor 3x^2 + 3x - 6

Step 1: Factor out a common factor from all terms if possible.

All terms have a common factor of 3. We start by factoring out the 3.

3x^2 + 3x - 6 =

= 3(x^2 + x - 2)

Step 2: We now need to deal with factoring x^2 + x - 2.

It is a trinomial of the form x^2 + ax + b, where the coefficient of x^2 is 1. To factor it, we need 2 numbers whose product is b and whose sum is a. In our case, we have x^2 + x - 2. We need two numbers whose product is -2 and whose sum is 1.

Pairs of numbers with product -2:

-2 and 1 since -2 * 1 = -2

-1 and 2 since -1 * 2 = -2

Now we add the two numbers in each line above.

-2 + 1 = -1    The sum is -1, but we need a sum of 1, so this is not it.

-1 + 2 = 1     Here we do get the sum of 1 that we need, so this pair of numbers is what we need.

The two numbers we need for factoring are -1 and 2.

Now we start the next step.

The factored trinomial will have this form.

= 3(x     )(x     )

All we need to do now is place each of the numbers in one of the blanks.

= 3(x - 1)(x + 2)

Answer: 3(x - 1)(x + 2)