Divide the polynomials. Express numbers using integers or simplified fractions. Check your answer by multiplication.
(8a^4b^5-6a3b^4+4a^2b^3-11)/(a^2b)
To divide the polynomials, we divide each term of the numerator by the denominator:
(8a^4b^5 - 6a^3b^4 + 4a^2b^3 - 11)/(a^2b)
Dividing the first term, 8a^4b^5, by a^2b, we get:
8a^2b^4
Dividing the second term, -6a^3b^4, by a^2b, we get:
-6ab^3
Dividing the third term, 4a^2b^3, by a^2b, we get:
4b^2
Finally, dividing the fourth term, -11, by a^2b, we get:
-11/(a^2b)
Putting everything together, the quotient is:
8a^2b^4 - 6ab^3 + 4b^2 - 11/(a^2b)
To check our answer, we can multiply the quotient by the denominator and see if we get the original polynomial:
(a^2b)(8a^2b^4 - 6ab^3 + 4b^2 - 11/(a^2b))
Multiplying each term by the denominator, we get:
8a^4b^5 - 6a^3b^4 + 4a^2b^3 - 11
Which is the same as the original polynomial. Therefore, our division is correct.