What happens if the remainder is zero in polynomial division?

What happens if the remainder is zero in polynomial division?

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). by x – 2. Use the result to find all zeros of f.

What is an expression that divides a polynomial without reminder?

Polynomial long division functions similarly to long division, and if the division leaves no remainder, then the divisor is called a factor.

What is meant if there is no remainder?

When one number divides another number completely, the remainder is 0. The remainder is always less than the divisor. If the remainder is greater than the divisor, it means that the division is incomplete. It can be greater than or lesser than the quotient….Examples:

What does the remainder mean in polynomial long division?

This illustrates the Remainder Theorem. If a polynomial f(x) is divided by x−a , the remainder is the constant f(a) , and f(x)=q(x)⋅(x−a)+f(a) , where q(x) is a polynomial with degree one less than the degree of f(x) . Synthetic division is a simpler process for dividing a polynomial by a binomial.

When we divide polynomials using long division when do we stop dividing explain?

Expert Answer When a divisor has more than one term or if the divisor is a polynomial containing more than one term, the four steps used to divide whole numbers— (divide, multiply, subtract, bring down the next term)—form the repetitive procedure for the polynomial long division.

How do you find the long division of a polynomial?

To verify if the polynomial division is correct, multiply the divisor with the quotient and add it to the remainder and check if it results in the dividend. If the dividend does not contain a term next to the highest degree, prefix a 0 as the coefficient to that term.