SOLUTION: factorise x^3-3x^2-4x+12

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Question 1130396: factorise x^3-3x^2-4x+12

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
start with x^3 - 3x^2 - 4x + 12

group the first 2 terms and the second 2 terms as shown below:

(x^3 - 3x^2) - (4x - 12)

factor out x^2 in the first part and factor out 4 in the second part to get:

x^2 * (x - 3) - 4 * (x - 3)

factor out the (x - 3) to get:

(x - 3) * (x^2 - 4)

since x^2 - 4 is equal to (x - 2) * (x + 2), you get:

(x - 3) * (x - 2) * (x + 2)

to test if this is good, take any random value of x and apply to the original form and the factored form.

i chose x = 5.

x^3 - 3x^2 - 4x + 12 = 125 - 75 - 20 + 12 = 42

(x - 3) * (x - 2) * (x + 2) = 2 * 3 * 7 = 42

you get the same value with both the original expression and the factored expression, so the factorization looks good.

i also graphed both expressions by setting them each equal to y and got the identical graph.

this is another way to see that you did it right.

my graph is shown below.