## What is P in Remainder Theorem?

The Remainder Theorem starts with an unnamed polynomial p(x), where “p(x)” just means “some polynomial p whose variable is x”. Then the Theorem talks about dividing that polynomial by some linear factor x – a, where a is just some number.

**How do you factor a polynomial using the remainder theorem?**

Remainder Theorem and Factor Theorem

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

### How do we use the remainder theorem to find P A?

Normally to find P(a) , one substitute x with a , but as we have to use Remainder theorem, we should divide P(x) by (x−a) and then the remainder would be P(a) . For this let us use synthetic division to divide 6×3−x2+4x+3 by (x−3) . i.e. while quotient is 6×2+17x+55 , remainder is 168 .

**Is remainder theorem and factor theorem same?**

Explanation: 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 formula of factor theorem?

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).

**What is factor theorem 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.

## How does remainder theorem work?

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 do you explain remainder theorem?**

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 the difference between remainder theorem and synthetic division?

You can use synthetic division whenever you need to divide a polynomial function by a binomial of the form x – c. Also, the Remainder Theorem states that the remainder that we end up with when synthetic division is applied actually gives us the functional value. Another use is finding factors and zeros.

**What is remainder theorem formula?**

The remainder theorem formula is: p(x) = (x-c)·q(x) + r(x). The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder.