Final Answer:
The quotient of 10t³ - 15t² divided by 5.
a. 10t² - 3t
Step-by-step explanation:
To find the quotient of 10t³ - 15t² divided by 5, divide each term by 5:
(10t³ - 15t²) / 5 = 10t³ / 5 - 15t² / 5
Simplify each term:
2t² - 3t
Therefore, the correct answer is a. 10t² - 3t.
In this context, dividing each term by 5 simplifies the expression, resulting in a polynomial in terms of t with coefficients that maintain the original expression's structure. The quotient 2t² - 3t represents the result of dividing 10t³ - 15t² by 5.
In conclusion, when dividing 10t³ - 15t² by 5, the quotient is 2t² - 3t, as represented by option a. This process adheres to the principles of polynomial division, simplifying the expression while preserving its mathematical integrity. OPTION A