What is r in factor theorem?

What is r in factor theorem?

The Remainder Theorem: When we divide a polynomial f(x) by x−c the remainder is f(c) So to find the remainder after dividing by x-c we don’t need to do any division: Just calculate f(c).

How do you solve a polynomial by factor theorem?

Factorization Of Polynomials Using Factor Theorem

1. Obtain the polynomial p(x).
2. Obtain the constant term in p(x) and find its all possible factors.
3. Take one of the factors, say a and replace x by it in the given polynomial.
4. Obtain the factors equal in no. to the degree of polynomial.
5. Write p(x) = k (x–a) (x–b) (x–c) …..

What are the 3 different polynomial theorems?

Theorems Used to Analyze Polynomial Functions

• Evaluate a polynomial using the Remainder Theorem.
• Use the rational zeros theorem to find rational zeros of a polynomial.
• Use the Factor Theorem to solve a polynomial equation.

How do you find the factor of FX?

If we divide a polynomial f(x) by (x – c), and (x – c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. Thus, according to this theorem, if the remainder of a division like those described above equals zero, (x – c) must be a factor.

What is factor theorem Class 9?

Factor Theorem. Factor Theorem. 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 factor theorem for polynomials?

If you get the remainder as zero, the factor theorem is illustrated as follows: The polynomial, say f (x) has a factor (x-c) if f (c)= 0, where f (x) is a polynomial of degree n, where n is greater than or equal to 1 for any real number, c.

Which theorem is used to analyze polynomial equations?

The Factor Theorem is another theorem that helps us analyze polynomial equations. It tells us how the zeros of a polynomial are related to the factors.

What is the factor of the polynomial if the remainder is 0?

x-a would be the factor of the polynomial if the r (x) i.e. remainder is 0. By the Remainder Theorem, Dividend = Divisor * Quotient + Remainder where P (x) = (x – a).

What is the converse of the factor theorem?

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. Also, we can say, if (x-a) is a factor of polynomial f (x), then f (a) = 0. This proves the converse of the theorem.