Question

HELLPP
Divide. A POLYNOMIAL BYA A MONOMIAL

Answer 1

7z^2/y -8z^4y -(9/2)z^2y^4

Explanation:

The quotient of division of a polynomial by a monomial is the sum of quotients of each of the terms divided by the monomial. "Simplify" in this context generally means that no common factors remain factored out.

Rules of exponents

The rules of exponents apply:

(a^b)/(a^c) = a^(b-c)

a^-b = 1/a^b

Division

The problem is effectively three (3) division/simplification problems.

`(-14z^4y^2+16z^6y^4+9z^4y^7)/(-2z^2y^3)=(-14z^4y^2)/(-2z^2y^3)+(16z^6y^4)/(-2z^2y^3)+(9z^4y^7)/(-2z^2y^3)\\\\=7z^(4-2)y^(2-3)-8z^(6-2)y^(4-3)-(9)/(2)z^(4-2)y^(7-3)=\boxed{(7z^2)/(y)-8z^4y-(9)/(2)z^2y^4}`

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Additional comment

We have elected to retain the original order of variables (z then y) and the original order of terms. Ordinarily, standard form would have the variables in alphabetical order (y then z) and the terms in order by decreasing degree. This order of terms also makes the leading coefficient positive. (The minus sign for a negative leading coefficient sometimes gets lost.)