Maharashtra State BoardSSC (English Medium) 9th Standard
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Factorize the Following Polynomial. - Algebra

Sum

Factorize the following polynomial.

(x2 – x)2 – 8 (x2 – x) + 12

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Solution

(x2 – x)2 – 8 (x2 – x) + 12

Let `x^2 - x = z`

`therefore (x^2 - x)^2 - 8 (x^2 - x) + 12`

`=z^2 - 8z + 12`

`= z^2 - 6z - 2z + 12`

= z (z - 6)- 2 (z - 6)

= (z - 6)(z - 2)

= (x2 - x - 6) (x2 - x - 2)     (Replace z = x2 - x)

= (x2 - 3x + 2x - 6) (x2 - 2x + x - 2)

= [x (x - 3) + 2 (x - 3)] [x (x - 2) + 1 (x - 2)]

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

Concept: Factor Theorem
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APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 3 Polynomials
Practice Set 3.6 | Q 2.1 | Page 55
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