Question

What is the quotient of (3d2-11d-4) and (d-4)? Assume the denominator does not
equal zero.

Answer 1

The quotient of the division of the polynomials (3d2 - 11d - 4) by (d - 4) is 3d + 1. This quotient is obtained through polynomial long division.

Step-by-step explanation:

The student has asked for the quotient of the polynomial division between (3d2 - 11d - 4) and (d - 4). To find the quotient, one can use polynomial long division or synthetic division, as both polynomials are in terms of d.

Upon performing polynomial long division, the steps are as follows:

1. Divide the first term of the dividend (3d2) by the first term of the divisor (d), which gives you 3d.
2. Multiply the entire divisor by this term and subtract the result from the dividend.
3. Bring down the next term of the dividend (-11d) and repeat the process until there are no terms left to bring down.
4. If you have a remainder, you express it as a fraction over the divisor. If there is no remainder, you have found the complete quotient.

The quotient for this division is 3d + 1, with no remainder.