Factor 6x3 + 5x2 – 18x – 15 (1 point)

well the way I see it it is

(6 x^3 - 18 x ) + (5 x^2 - 15)

which is

6 x ( x^2 - 3) + 5 (x^2 - 3)

get it ?

To factor the expression 6x^3 + 5x^2 - 18x - 15, we need to look for common factors and grouping. First, let's examine all the terms to find the greatest common factor (GCF).

Step 1: Find the GCF of all terms
The coefficients are 6, 5, -18, and -15. The GCF of these numbers is 1.

The variables in each term are x^3, x^2, x, and no x. The variable x is common to all terms, and the lowest exponent is x. So, the GCF is x.

Step 2: Factor out the GCF
Now, we can factor out the GCF from all the terms:
1x(6x^3/1x + 5x^2/1x - 18x/1x - 15/1x)

Simplifying this, we get:
x(6x^2 + 5x - 18 - 15/x)

Step 3: Factor the remaining expression
Now, we focus on factoring the expression inside the parentheses: 6x^2 + 5x - 18.

We can use various factoring techniques like grouping, quadratic formula, or factoring by inspection. However, in this case, the expression does not factor nicely using these methods. Therefore, we can conclude that the given expression 6x^3 + 5x^2 - 18x - 15 does not factor further.

Therefore, the final factored form is:
x(6x^2 + 5x - 18)