Chapter 11.3, Problem 5LC

To determine

How is dividing polynomials like dividing real numbers and how is it different.

Explanation of Solution

Concept Used:

If an expression of smaller degree divides another expression completely, then the divisor expression will be a factor of the dividend expression.

Calculation:

While dividing a polynomial with other lower degree polynomial using the long division method, we use the same process as we use to divide the real numbers using the long division.

In order to divide the polynomial, in each step we divide the leading term of dividend by the leading term of the divisor and that gives the quotient for that step.

If the divisor expression divides the dividend expression completely, then the divisor expression will be a factor of the dividend expression. That is, if on dividing the dividend with the divisor expression, the remainder is zero, then the divisor expression will be a factor of the dividend expression.