Final answer:
The polynomial (35h³ - 63h) divided by the monomial 7h² results in 5h - 9/h. The process involves dividing the coefficients and subtracting the exponents of the variables. There is no remainder as the division yields a whole number and a proper fraction.
Step-by-step explanation:
To solve the mathematical problem completely, we need to divide the polynomial expression by the given monomial. The problem asks us to divide (35h³ - 63h) / 7h². To do that, we follow the rules of division of exponentials, which require us to divide the coefficients and subtract the exponents of the variables.
First, we divide each term of the polynomial by the monomial:
- Divide 35h³ by 7h². This gives us 5h (since 35 divided by 7 equals 5 and h³ divided by h² gives us h).
- Next, divide -63h by 7h². Since the degree of h in the denominator is higher than in the numerator, the result is a fraction. -63 divided by 7 gives us -9, and h divided by h² simplifies to 1/h.
Therefore, the quotient is 5h - 9/h. There is no need to include a remainder since the division results in a whole number and a proper fraction. Lastly, we should always check the answer to ensure it is reasonable, which in this case, confirms the division is performed correctly. The division by the variable with a higher power resulting in a proper fraction is a key concept.