What does it mean when you divide polynomials and the remainder is zero?

The Remainder Theorem states that f(c) = the remainder. So if the remainder comes out to be 0 when you apply synthetic division, then x – c is a factor of f(x).

Can you use the Remainder Theorem if the remainder is 0?

Remember that when a polynomial is divided by a “factor”, the remainder is zero. We simply need to use the Remainder Theorem to see if the remainder is zero. The remainder is 0, so (x + 4) is a factor.

What does it mean when the Remainder Theorem is verified?

The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x – a, the remainder of that division will be equivalent to f(a). It should be noted that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x – number.

How does long division of polynomials work?

The result R = 0 occurs if and only if the polynomial A has B as a factor. Thus long division is a means for testing whether one polynomial has another as a factor, and, if it does, for factoring it out. For example, if a root r of A is known, it can be factored out by dividing A by (x – r).

How does Remainder Theorem help us find the zeros of a polynomial function?

The Factor Theorem is another theorem that helps us analyze polynomial equations. It tells us how the zeros of a polynomial are related to the factors. Similarly, if x−k is a factor of f(x) , then the remainder of the Division Algorithm f(x)=(x−k)q(x)+r f ( x ) = ( x − k ) q ( x ) + r is 0.

What is the factor theorem on polynomial long division?

According to the Factor Theorem: If we divide a polynomial f(x) by (x – c), and (x – c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. If the remainder of such a division is not zero, then (x – c) is not a factor.

How do you find the oblique asymptote of 1?

The oblique or slant asymptote is found by dividing the numerator by the denominator. A slant asymptote exists since the degree of the numerator is 1 greater than the degree of the denominator. 2 2. 1 2 1 2 1 2. 1 2 4 | 0 9 2 29 24 5 The quotient is 1 with a remainder of 5. The equation 1 is a slant asymptote.

How do you find the asymptote of a function?

For rational functions, oblique asymptotes occur when the degree of the numerator is one more than the degree of the denominator. In such a case the equation of the oblique asymptote can be found by long division. Use this Slant asymptote calculator to make your oblique asymptote calculations easier.

What is a slant asymptote in math?

Oblique Asymptote or Slant Asymptote happens when the polynomial in the numerator is of higher degree than the polynomial in the denominator. It is a slanted line that the function approaches as the x approaches infinity or minus infinity.

Do asymptotes appear on the AP Calculus exams?

(The answer to the last question is yes. Asymptotes definitely show up on the AP Calculus exams ). Of the three varieties of asymptote — horizontal, vertical, and oblique — perhaps the oblique asymptotes are the most mysterious.