Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 106 views

    Factorization of Polynomials

    Uploaded by

    minal bhatt
    This document discusses two methods for factorizing quadratic polynomials: 1) Splitting the middle term. This involves finding two numbers whose sum is the coefficient of x and whose product is the constant term. 2) Using the factor theorem. This involves finding two numbers p and q that make the polynomial equal to 0 when substituted in place of x. These numbers p and q will be factors of the polynomial. As an example, the polynomial x^2 + 5x + 6 is factorized by splitting the middle term into (x + 2)(x + 3). The polynomial x^2 - 3x + 2 is factorized using the factor theorem into (x - 2)(x - 1).

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Factorization of Polynomials

    Uploaded by

    minal bhatt
    106 views1 page
    This document discusses two methods for factorizing quadratic polynomials: 1) Splitting the middle term. This involves finding two numbers whose sum is the coefficient of x and whose product is the constant term. 2) Using the factor theorem. This involves finding two numbers p and q that make the polynomial equal to 0 when substituted in place of x. These numbers p and q will be factors of the polynomial. As an example, the polynomial x^2 + 5x + 6 is factorized by splitting the middle term into (x + 2)(x + 3). The polynomial x^2 - 3x + 2 is factorized using the factor theorem into (x - 2)(x - 1).

    Original Description:

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    This document discusses two methods for factorizing quadratic polynomials: 1) Splitting the middle term. This involves finding two numbers whose sum is the coefficient of x and whose product is the constant term. 2) Using the factor theorem. This involves finding two numbers p and q that make the polynomial equal to 0 when substituted in place of x. These numbers p and q will be factors of the polynomial. As an example, the polynomial x^2 + 5x + 6 is factorized by splitting the middle term into (x + 2)(x + 3). The polynomial x^2 - 3x + 2 is factorized using the factor theorem into (x - 2)(x - 1).

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    106 views1 page

    Factorization of Polynomials

    Uploaded by

    minal bhatt
    This document discusses two methods for factorizing quadratic polynomials: 1) Splitting the middle term. This involves finding two numbers whose sum is the coefficient of x and whose product is the constant term. 2) Using the factor theorem. This involves finding two numbers p and q that make the polynomial equal to 0 when substituted in place of x. These numbers p and q will be factors of the polynomial. As an example, the polynomial x^2 + 5x + 6 is factorized by splitting the middle term into (x + 2)(x + 3). The polynomial x^2 - 3x + 2 is factorized using the factor theorem into (x - 2)(x - 1).

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 1

    6/8/2020 Factorization of Polynomials

    Factorisation of Quadratic Polynomials- Splitting the middle term

    Factorisation of the polynomial ax 2


    + bx + c by splitting the middle term is as follows:

    Step 1: We split the middle term by finding two numbers such that their sum is equal to the
    coefficient of x and their product is equal to the product of the constant term and the
    coefficient of x . 2

    For example for the quadratic polynomial (x 2


    + 5x + 6) the middle term can be split as,
    x + 2x + 3x + 6 
    2

    Here,2 + 3 = 5 and 2 × 3 = 6.

    Step 2: Now, we factorise by pairing the terms and taking the common factors.
    2
    x + 2x + 3x + 6

    = x(x + 2) + 3(x + 2)

    = (x + 2)(x + 3)

    Thus, x + 2 and x + 3 are factors of x 2


    + 5x + 6 .

    Factorisation of Quadratic Polynomials - Factor theorem

     
    To factorise a quadratic polynomial f (x) = ax + bx + c, find two numbers p and q such that
    2

    f (p) = f (q) = 0. Let us factorise the quadratic polynomial f (x) = x − 3x + 2.


    2

    (i) f (2) = 2 − 3(2) + 2 = 4 − 6 + 2 = 0


    2

    Hence, x − 2 is a factor of x − 3x + 2. 2

    (ii) f (3) = 3 2
    − 3 × 3 + 2 = 9 − 9 + 2 = 2 ≠ 0

    Hence, x − 3 is not a factor of x 2


    − 3x + 2 .

    (iii) f (1) = 1 2
    − 3 × 1 + 2 = 0

    Hence, x − 1 is a factor of x − 3x + 2. 2

    So, x − 1 and x − 2 are the factors of the quadratic polynomial x 2


    − 3x + 2 .
    2
    x − 3x + 2 = (x − 2)(x − 1)

    https://learn.byjus.com/revision-summaries/22271 1/1

    You might also like