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.