Question

You divide two polynomials and obtain the result x^2- 3 + 6/x+1 What is the dividend? How did you find it?

Answer 1

The dividend is determined by multiplying the divisor (x + 1) by the quotient (x^2 - 3) and then adding the remainder (6). The final dividend is x^3 + x^2 - 3x + 3.

Step-by-step explanation:

To determine the dividend when given the result of polynomial division, you can multiply the divisor by the quotient and then add the remainder. The expression given in the question, x^2- 3 + 6/(x+1), suggests that the quotient is x^2 - 3 and the remainder is 6, with the divisor being x + 1. Therefore, to find the original dividend, you follow these steps:

• Multiply the quotient x^2 - 3 by the divisor x + 1.
• Add the remainder 6 to the result of the multiplication.

Through this process, the dividend would be obtained:

1. Multiplication: (x^2 - 3)(x + 1) which simplifies to x^3 + x^2 - 3x - 3.
2. Addition of remainder: x^3 + x^2 - 3x - 3 + 6.

Combining like terms, the final expression for the dividend is x^3 + x^2 - 3x + 3.