MathsPolynomialsFactors PartClass 9 Factorization of a polynomial | What are Zeroes of a polynomial?

Class 9 Factorization of a polynomial | What are Zeroes of a polynomial?

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    • Factorization of Polynomials
    • Zero of a polynomial
    • Summary
    • What’s Next?

    In the previous segment, we learned how to find the factors of a number. In this segment, we will learn about the factorization of a polynomial.

    How do we find the factors of a polynomial?

    If a polynomial can be written as a product of two polynomials, then these are known as the factors of the original polynomial.

    Each factor of a polynomial shows the following characteristics:

    • The degree will be less than the degree of the polynomial.
    • It cannot be factorized further.

    For example, Consider ?2 + 3? + 2.

    ?2 + 3? + 2 = (x+1)(x+2)

    Thus, (x+1) and (x+2) are the factors of (?2 + 3? + 2

    • (x+1) and (x+2) have degree 1, which is less than that of the polynomial which has degree 2.
    • (x + 1) and (x+2) are in the simplest form and cannot be factorised further.

    What are the Zeroes of a polynomial?

    • Zero of a polynomial is a number when substituted in place of the variable gives the value of the polynomial equal to zero.
    • In some cases, factorisation helps to get the zeroes of the polynomial.

    For example,

    (x+1) and (x+2) are the factors of ?2 + 3? + 2

    The opposite of the numbers +1 and +2 are -1 and -2 respectively. Thus, the zeroes of the polynomial ?2 + 3? + 2are -1 and -2.

    These two numbers are called the zeroes of the polynomial. Substituting either of these values in ?2 + 3? + 2will give zero.

    Also Read:

    How do we Factorise Polynomials using Identities? Part 1

    How do we Factorise Polynomials using Identities? Part 2

    How do we Factorise Polynomials using Identities? Part 3

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