Answer :
The polynomial 6x⁴ + 21x³ + 18x² can be factored by first factoring out the common factor, which is 3x². The resulting polynomial 2x² + 7x + 6 can further be factored into (2x + 3)(x + 2). Therefore, the fully factored form is 3x²(2x + 3)(x + 2).
The polynomial given, 6x⁴ + 21x³ + 18x², can be factored by first factoring out a common factor among all the terms. The common factor here is 3x², leaving 2x² + 7x + 6. This new polynomial can further be factored into (2x + 3)(x + 2). So the entire factored form of the polynomial is: 3x²(2x + 3)(x + 2).
Here's how we reached this solution step by step:
- Identify the greatest common factor, in this case, 3x².
- Divide each term by 3x² to get a reduced polynomial: 2x² + 7x + 6.
- Factor that polynomial. In doing so, we ended up with (2x + 3)(x + 2).
These steps demonstrate the thought process and approach to factoring polynomials effectively.
Learn more about Factoring Polynomials here:
https://brainly.com/question/35418869
#SPJ11
