FACTOR THE EXPRESSION COMPLETELY
9x^3 + 36x^2 - x - 4
9x^3 + 36x^2 - x - 4
9x^2(x+4) - (x+4)
factor out the common (x+4), then you will have a difference of two squares (9x^2-1) which will factor
To factor the given expression completely, follow these steps:
Step 1: Look for common factors.
In this case, there are no common factors among all the terms.
Step 2: Check for a common factor among pairs of terms.
Factor out the greatest common factor (GCF) if there is one.
The GCF of the coefficients 9, 36, -1, and -4 is 1, so we won't factor it out.
Step 3: Try factoring by grouping.
Group the terms to see if any common factors can be factored out.
9x^3 + 36x^2 - x - 4
Rearranging the terms:
(9x^3 + 36x^2) + (-x - 4)
Taking out the common factors from each grouping:
9x^2(x) + 4(9x^2) - (x + 4)
Simplifying:
9x^2(x + 4) - (x + 4)
Step 4: Factor out the common binomial factor.
We have a common binomial factor of (x + 4).
(x + 4)(9x^2 - 1)
Step 5: Check for further factoring.
Note that 9x^2 - 1 is a difference of squares, which can be factored as (3x - 1)(3x + 1).
Therefore, the expression 9x^3 + 36x^2 - x - 4 can be factored completely as:
(x + 4)(3x - 1)(3x + 1)