Factoring a product of a quad Factor completely. 4x^(5)+18x^(4)+18x^(3)

Answer: 4x^5 + 18x^4 + 18x^3 = 2x^3(2x + 3)(x + 3)

The given expression is:

4x^5 + 18x^4 + 18x^3

First, we can factor out the greatest common factor (GCF) of the three terms, which is 2x^3:

2x^3(2x^2 + 9x + 9)

The expression 2x^2 + 9x + 9 can be factored using the quadratic formula, completing the square, or by recognizing that it is of the form ax^2 + bx + c, where a = 2, b = 9, and c = 9. We can then factor it as the product of two binomials:

2x^3(2x + 3)(x + 3)

Therefore, the fully factored form of the expression is:

4x^5 + 18x^4 + 18x^3 = 2x^3(2x + 3)(x + 3)