# What is remainder factor theorem?

## What is remainder factor theorem?

The remainder factor theorem is actually two theorems that relate the roots of a polynomial with its linear factors. The theorem is often used to help factorize polynomials without the use of long division. Especially when combined with the rational root theorem, this gives us a powerful tool to factor polynomials.

## What do the the remainder and factor theorems state?

The Factor and Remainder Theorems If p(x) is a polynomial of degree 1 or greater and c is a real number, then when p(x) is divided by x−c, the remainder is p(c). If x−c is a factor of the polynomial p, then p(x)=(x−c)q(x) for some polynomial q. Then p(c)=(c−c)q(c)=0, showing c is a zero of the polynomial.

**What is factor theorem and remainder theorem Class 9?**

x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number. This is an extension to remainder theorem where remainder is 0, i.e. p(a) = 0.

**What is the difference between remainder and factor theorem?**

The remainder theorem tells us that for any polynomial f(x) , if you divide it by the binomial x−a , the remainder is equal to the value of f(a) . The factor theorem tells us that if a is a zero of a polynomial f(x) , then (x−a) is a factor of f(x) , and vice-versa.

### 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).

### What is remainder theorem in Class 9?

Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). Proof: Let p(x) be any polynomial with degree greater than or equal to 1.

**What is the importance of the remainder theorem and factor theorem?**

The remainder theorem and factor theorem are very handy tools. They tell us that we can find factors of a polynomial without using long division, synthetic division, or other traditional methods of factoring. Using these theorems is somewhat of a trial and error method.

**What is remainder theorem Class 9?**

#### What is factor theorem explain with example?

Answer: An example of factor theorem can be the factorization of 6×2 + 17x + 5 by splitting the middle term. In this example, one can find two numbers, ‘p’ and ‘q’ in a way such that, p + q = 17 and pq = 6 x 5 = 30. After that one can get the factors. For example, x + 2 is a factor belonging to the polynomial x2 – 4.

#### What is remainder theorem Class 10?

The remainder theorem definition states that when a polynomial f(x) is divided by the factor (x -a) when the factor is not necessarily an element of the polynomial, then you will find a smaller polynomial along with a remainder.

**What is remainder theorem for Class 10?**

According to the remainder theorem, if is divided by then, the remainder is given by, If is divided by , then the remainder is given by, Hence, a polynomial when divided by leaves a remainder 3 and when divided by leaves a remainder 1. Then if the polynomial is divided by , it leaves a remainder .

**What is the formula of factor theorem?**

What is the Factor Theorem Formula? As per the factor theorem, (y – a) can be considered as a factor of the polynomial g(y) of degree n ≥ 1, if and only if g(a) = 0. Here, a is any real number. The formula of the factor theorem is g(y) = (y – a) q(y).