What is Class 9 polynomial factorization?

Factorisation of Polynomials Let p(x) be a polynomial of degree n ≥ 1 and a be any real number such that, (i) p(a) = 0, then (x − a) is a factor of p(x) conversely, (ii)If (x − a) is a factor of p(x), then p(a) = 0.

How do you Factorise factor theorem Class 9?

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 is meant by factorisation of polynomials?

Definitions: Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying. To factor polynomials, we generally make use of the following properties or identities; along with other more techniques.

What is factorization example?

Example: (x+2)(x+3) = x2+ 2x + 3x + 6 = x2+ 5x + 6. Here, 5 = 2 + 3 = d + e = b in general form and 6 = 2 × 3 = d × e = c in general form. To factorize quadratic polynomial, we shall be looking for numbers which on multiplication will get equal to c and on summation equal to b. Example: Factorize x2+8x+12.

Which chapter is polynomial Class 9 in RD Sharma?

Mathematics NCERT Grade 9, Chapter 2: Polynomials: Polynomials are a particular type of algebraic expression. Students will also study the remainder theorem and factor theorem in this chapter. Some more algebraic identities will be discussed in this chapter.

What is the formula for Factorisation?

The general factorization formula is expressed as N = Xa × Yb × Zc. Here, X, Y, Z represent the factors of a factorized number.

What is factor theorem Class 9 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.

How do you factor a cubic polynomial class 9?

Factorising Cubic Polynomial

  1. Find x = a where p(a) = 0.
  2. Then (x – a) is the factor of p(x)
  3. Now divide p(x) by (x – a) i.e. (p(x))/((x – a))
  4. And then we factorise the quotient by splitting the middle term.

What is the formula for factorization?

What is the process of factorisation?

Factorisation is a method of breaking the arithmetic algebraic expressions into the product of their factors. If we multiply the factors again, then they will result in original expression.

What is remainder theorem Class 9?

The Remainder Theorem Definition states that when a polynomial is p ( a ) is divided by another binomial ( a – x ), then the remainder of the end result that is obtained is p ( x ).