Final answer:
To find the product of (5x² +x+5)(3x+5), use vertical multiplication, multiply each term of the first polynomial by every term of the second, and combine like terms to get the final result, which is 15x³ + 28x² + 20x + 25.
Step-by-step explanation:
The product of the two polynomials (5x² +x+5)(3x+5) can be found using vertical multiplication, which is akin to the process used for multiplying numbers, but applies to algebraic expressions as well. In this process, each term of the first polynomial is multiplied by each term of the second polynomial, and then the results are combined. Here is the step-by-step calculation:
- Multiply 5x² by 3x to get 15x³.
- Multiply 5x² by 5 to get 25x².
- Multiply x by 3x to get 3x².
- Multiply x by 5 to get 5x.
- Multiply 5 by 3x to get 15x.
- Multiply 5 by 5 to get 25.
Next, we add up the like terms:
- 15x³ remains unchanged.
- Combine 25x² and 3x² to get 28x².
- Combine 15x and 5x to get 20x.
- 25 remains unchanged.
Therefore, the product of the two polynomials is 15x³ + 28x² + 20x + 25.