To find the quotient of the polynomial 3x² + 17x + 10 when it is divided by 5, we will perform polynomial division.
First, let’s rewrite the polynomial:
- 3x² is the term of degree 2.
- 17x is the term of degree 1.
- 10 is the constant term.
Next, we will divide each term of the polynomial by 5:
- The first term: 3x² ÷ 5 becomes (3/5)x².
- The second term: 17x ÷ 5 becomes (17/5)x.
- The third term: 10 ÷ 5 becomes 2.
Putting it all together, the quotient of the expression 3x² + 17x + 10 when divided by 5 is:
3 --- (3/5)x² + (17/5)x + 2 5
Thus, the final result can be written as:
Quotient: (3/5)x² + (17/5)x + 2
This means that when you divide the polynomial 3x² + 17x + 10 by 5, you obtain (3/5)x² + (17/5)x + 2 as the quotient. This process can be particularly useful in scenarios where polynomial manipulation is required in algebra and calculus.