What is remainder theorem explain with an example?
Remainder Theorem : If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x – a, then the remainder is p(a). Example : 2×2−5x−1 divided by x-3. f(x) is 2×2−5x−1.
How is remainder theorem used in real life?
Real-life Applications The remainder theorem provides a more efficient avenue for testing whether certain numbers are roots of polynomials. This theorem can increase efficiency when applying other polynomial tests, like the rational roots test.
What is the relationship between remainder and factor theorem?
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 statement of factor theorem?
The factor theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and ‘a’ is any real number, then (x – a) is a factor of f(x) if f(a) = 0. In other words, we can say that (x – a) is a factor of f(x) if f(a) = 0.
What is the importance of remainder theorem?
The remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the division algorithm.
Why is remainder theorem important?
The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily.
What is factor theorem Class 10?
In mathematics, factor theorem is used when factoring the polynomials completely. It is a theorem that links factors and zeros of the polynomial. According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
What is remainder theorem Class 9 examples?
It is applied to factorize polynomials of each degree in an elegant manner. For example: if f(a) = a3-12a2-42 is divided by (a-3) then the quotient will be a2-9a-27 and the remainder is -123. Thus, it satisfies the remainder theorem.
What would you consider as remainders in your life?
Remainder is the general word ( the remainder of one’s life ); it may refer in particular to the mathematical process of subtraction: 7 minus 5 leaves a remainder of 2.
How is the remainder theorem used or applied?
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.
What is the remainder when 4444 4444 divided by 9?
Such type of questions can be solved by observing a pattern. So, for k = 4444, remainder is 7. The correct option is C.
What is remainder theorem Class 10 ICSE?
By remainder theorem we know that when a polynomial f (x) is divided by x – a, then the remainder is f(a). Thus, (x + 1) is a factor of the polynomial f(x). Thus, (2x – 1) is not a factor of the polynomial f(x). Thus, (x + 2) is a factor of the polynomial f(x).
Why is the factor theorem useful?
Factor theorem is usually used to factor and find the roots of polynomials. A root or zero is where the polynomial is equal to zero. Therefore, the theorem simply states that when f(k) = 0, then (x – k) is a factor of f(x).
What is remainder theorem Class 9 Ncert?
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).
What are 3 ways mathematicians can interpret remainders?
Learn how to interpret the remainder in 3 different ways (ignore it, round it, or report it as a fraction or decimal).
What is the importance of factor theorem?
What is the Importance of the Factor Theorem? Factor theorem is mainly used to factor the polynomials and to find the n roots of that polynomial. It is a special kind of the polynomial remainder theorem that links the factors of a polynomial and its zeros.