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To divide the polynomial 6x^4 + 3x^3 - 7 by the monomial x^2, we can rewrite it as a fraction:
(6x^4 + 3x^3 - 7) / x^2
Now, let's simplify this expression by breaking it down into two separate terms:
6x^4 / x^2 + 3x^3 / x^2 - 7 / x^2
Simplify each term separately:
= 6x^(4-2) + 3x^(3-2) - 7x^(-2)
= 6x^2 + 3x - 7/x^2
So, the division of the polynomial by the monomial denominator is equal to:
6x^2 + 3x - 7/x^2