1 / 6

FACTORISATION

FACTORISATION. DEFINITION:- The resolution of an integer or polynomial into factors such that when multiplied together they give the integer or polynomial. Prep II Mathematics Mr. Naveed-ur- Rehman March 07, 2011. FACTORISATION BY TAKING COMMON. Examples:- 2x 2 -6x = 2x(x-3)

ozzy
Download Presentation

FACTORISATION

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. FACTORISATION DEFINITION:- The resolution of an integer or polynomial into factors such that when multiplied together they give the integer or polynomial Prep II Mathematics Mr. Naveed-ur- Rehman March 07, 2011

  2. FACTORISATION BY TAKING COMMON Examples:- • 2x2-6x = 2x(x-3) • 4y3+12y2-2y = 2y(2y2+6y-1) • 3x-6y+12z = 3(x-2y+4) First of all we take common if it exists.

  3. FACTORISATION BY TAKING TWO AND TWO COMMON Examples:- • a2-ab+2a-2b = (a2-ab)+(2a-2b) = a(a-b)+2(a-b) = (a-b)(a+b) • X3-x2+x-1 = x2(x-1)+(x-1) =(x-1)(x2+1) If there is no thing common in whole expression, then we look either any thing common in group of two and two values or not, if it exists we take common.

  4. FACTORISATION BY USING ALGEBARICIDENTITIES Examples:- • 4x2+12x+9 = (2x)2+2(2x)(3)+(3)2 = (2x+3)2 • X2-4x+4 = (x)2-2(x)(2)+(2)2 = (x-2)2 • 4x2-16 = (2x)2-(4)2 = (2x+4)(2x-4) In this method, we use algebaric identities such as: (a+b)2 = a2+2ab+b2 2. (a-b)2 = a2-2ab+b2 3. a2-b2 = (a+b)(a-b)

  5. FACTORISATION BY BREAKING MIDDLE TERM (2x)(4x)= 8x2 2x+4x =6x Examples:- x2+6x+8 = x2+2x+4x+8 = x(x+2)+4(x+2) = (x+2)(x+4) x2-11x+24 = x2-3x-8x+24 = x(x-3)-8(x-3) = (x-3)(x-8) a2+2a-8 = a2+4a-2a-8 = a(a+4)-2(a+4) = (a+4)(a-2) The quadratic expression for which perfect square formulae are not applicable, than we find factors by break middle term such that: For ax2+bx+c Product of factors = (ax2)(c) Addition of factors = bx (-3x)(-8x) =24x2 (-3x)+(-8x) =-11x (4a)(-2a) = -8a2 (4a)+(-2a) =2a

  6. CONCLUSION • It is expected that students will learn factorisation in easy way. • Students will solve problems including quadratic equations.

More Related