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What are the two methods of dividing polynomials?

There are two methods in mathematics for dividing polynomials. These are the long division and the synthetic method.

Are the steps in dividing polynomials helpful Why?

Answer. Answer: Yes, so we can understand the process of solving and we can find the exact answer.

What is the quotient in the remainder theorem?

A= B * Q + R where 0 ≤ R < B When we divide A by B in long division, Q is the quotient and R is the remainder.

What is Remainder Theorem Class 9 formula?

The remainder theorem states that when a polynomial f(x) is divided by a linear polynomial (x−a) then the remainder of that division will be equal to f(a). 7 divided by 2 equals 3 with remainder 1, where 7 is dividend, 2 is divisor, 3 is quotient and 1 is remainder. ∴7=2×3+1. ∴f(x)÷d(x)=q(x) with a remainder r(x).

What is meant by Remainder Theorem?

: a theorem in algebra: if f(x) is a polynomial in x then the remainder on dividing f(x) by x − a is f(a)

Why is the remainder theorem important?

The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily.

How do you do remainder and factor theorem?

Remainder Theorem and Factor Theorem

  1. f(x) ÷ d(x) = q(x) with a remainder of r(x)
  2. f(x) = (x−c)·q(x) + r(x)
  3. f(x) = (x−c)·q(x) + r.

What does the factor theorem tell us?

The proof of The Factor Theorem is a consequence of what we already know. If (x−c) is a factor of p(x), this means p(x)=(x−c)q(x) for some polynomial q. Of the things The Factor Theorem tells us, the most pragmatic is that we had better find a more efficient way to divide polynomials by quantities of the form x−c.

What is the meaning of factor theorem?

In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if (i.e. is a root).