To factorize the expression 5x³ + 135 + 5x + 3x² + 9, we will start by grouping and simplifying the terms.
The expression can be rearranged for clarity:
- 5x³
- + 3x²
- + 5x
- + 135
- + 9
Next, we can try to group the terms:
- (5x³ + 3x² + 5x) + (135 + 9)
This gives us:
- 5x(x² + rac{3}{5}x + 1) + 144
Now we can look for common factors in the grouped terms. Notice that 135 and 9 can be simplified:
- 135 + 9 = 144
Finding the GCD (greatest common divisor), we can rewrite the expression as follows:
- 5x³ + 3x² + 5x + 144
From this point, we can try factoring further or using the quadratic formula if needed, but in this case, the common approach is to see if the cubic term can be factored more simply or needs numerical factoring instead.
The final factorization process might include completing square for the quadratic or using synthetic division. Therefore, the expression is better understood as:
- While it can’t be cleanly factored further with integers, it represents a polynomial that can be explored using numerical methods if roots are needed.
In conclusion, while it seems complex at first glance, understanding how to group and rearrange terms is key to navigating polynomials. For most practical purposes, recognizing the form of the expression and applying the appropriate factorization strategies can lead you to solutions.