Factor. 18x^3+24x^2-45x

It's more basic than you think.

3x(6x^2 + 8x - 15)

Can't factor out anything else, therefore this is the simplified form.

To factor the expression 18x^3 + 24x^2 - 45x, we can find the greatest common factor (GCF) of all the terms and then factor it out.

Step 1: Find the GCF:
- The coefficient of 18x^3, 24x^2, and -45x is 3.
- The variable x appears in each term with the exponent of the smallest power, which is x^1.
Therefore, the GCF is 3x.

Step 2: Divide each term by the GCF:
Dividing each term by 3x, we obtain:
(18x^3)/(3x) + (24x^2)/(3x) - (45x)/(3x)

Simplifying this, we get:
6x^2 + 8x - 15

Step 3: Factor the simplified expression:
Now, we can try to factor the expression 6x^2 + 8x - 15. To do this, we are looking for two binomials that multiply together to give us 6x^2 + 8x - 15.

Since the leading coefficient is positive (6), we know that the signs in the factors should either both be positive or both be negative.

Let's look for two binomials in the form (ax + b)(cx + d) and try to find values for a, b, c, and d that satisfy the equation. The only combination that works for this expression is:
(2x + 5)(3x - 3)

Step 4: Write the factored form:
Finally, we can write the factored form of the original expression by combining the GCF and the factored form of the simplified expression:
18x^3 + 24x^2 - 45x = 3x(2x + 5)(3x - 3)

So, the factored form of 18x^3 + 24x^2 - 45x is 3x(2x + 5)(3x - 3).