Keywords:
Division, quotient, polynomial, monomial
For this case we must solve a division between a polynomial and a monomial and indicate which is the quotient.
By definition, if we have a division of the form: \(\frac {a} {b} = c\), the quotient is given by "c".
We have the following polynomial:
\(65y ^ 3 + 15y ^ 2 - 25y\) that must be divided between monomy\(5y\), then:
\(C (y)\) represents the quotient of the division:
\(C (y) = \frac {65y ^ 3 + 15y ^ 2 - 25y} {5y}\)
\(C (y) = \frac {65y ^ 3} {5y} + \frac {15y ^ 2} {5y} - \frac {25y} {5y}\)
\(C (y) = 13y ^ 2 + 3y-5\)
Thus, the quotient of the division between the polynomial and the monomial is given by:
\(C (y) = 13y ^ 2 + 3y-5\)
Answer:
The quotient is: \(C (y) = 13y ^ 2 + 3y-5\)
Option: A
