Divide the polynomials. Express numbers using integers or simplified fractions. Check your answer by multiplication.
(8a^4b^56a3b^4+4a^2b^3-11)/(a^2b)
To divide the polynomials, we first divide each term in the numerator by the denominator.
The first term is (8a^4b^5 * 6a^3b^4) / (a^2b) = 48a^7b^9/a^2b = 48a^5b^8.
The second term is (4a^2b^3) / (a^2b) = 4b^2.
The third term is (-11) / (a^2b) = -11 / (a^2b).
So, the polynomial is divided as: 48a^5b^8 + 4b^2 - 11/(a^2b).
To check the answer, we can multiply the divisor (a^2b) by the quotient we obtained.
(a^2b)(48a^5b^8) = 48a^7b^9.
(a^2b)(4b^2) = 4a^2b^3.
(a^2b)(-11/(a^2b)) = -11.
Adding the results of the multiplication: 48a^7b^9 + 4a^2b^3 - 11.
As the result matches the numerator of the original polynomial, our division is correct.