Solve the following inequality
X^3 - x^2 >6x
Answers
x
(
x
2
−
x
−
6
)
x
(
x
−
3
)
(
x
+
2
)
Explanation:
x
3
−
x
2
−
6
x
1) Simplify the polynomial.
( What does each term have in common? )
In this case, they each have
1
x
or
x
in common
2) Place the extraneous parts on the outside.
(Put what you just simplified outside the parentheses)
In this example, that means
x
x
(
x
2
−
x
−
6
)
3) Factor the trinomial.
(Just like you usually would)
I was taught to think of a number that multiplies to make the last number (
6
) and add together to make the middle coefficient (
1
). When you do that you get
−
3
and
2
. So, the answer is:
x
(
x
−
3
)
(
x
+
2
)
Notes:
- You should always simplify before you begin factoring because it makes it easier and faster.
- You can always check you answer by multiplying the equation back out again. If you did it right, you should get what you started with