Math, asked by sakshampatel0, 4 months ago

x^2/4+y^2/9+xy/3 factorise middle term splitting

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Answered by AarnaShah
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Answer:

How To Factorise A Polynomial By Splitting The Middle Term

December 22, 2020 by Veerendra

Factorise A Polynomial By Splitting The Middle Term Example Problems With Solutions

Type I: Factorization of Quadratic polynomials of the form x2 + bx + c.

(i) In order to factorize x2 + bx + c we have to find numbers p and q such that p + q = b and pq = c.

(ii) After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

Example 1:    Factorize each of the following expressions:

(i) x2 + 6x + 8               (ii) x2 + 4x –21

Solution:

(i) In order to factorize x2  + 6x + 8, we find two numbers p and q such that p + q = 6 and pq = 8.

Clearly, 2 + 4 = 6 and 2 × 4 = 8.

We know split the middle term 6x in the given quadratic as 2x + 4x, so that

x2    + 6x + 8 = x2  + 2x + 4x + 8

= (x2  + 2x) + (4x + 8)

= x (x + 2) + 4 (x+ 2)

= (x + 2) (x + 4)

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