The document focuses on the methods of factorization in algebra, explaining how to express algebraic expressions as products of factors. It covers techniques such as common factors, regrouping, and using algebraic identities for simplification. Various examples are provided to illustrate these concepts.

1. CH- 14
FACTORISATION
Prepared By-
Anoop Singh Yadav
TGT Maths
JNV Bhiwani

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sronOUre‹+TR
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• >avrs oac«oes or «<e wcieas y•+
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3. e.g. 9O = 2 .x 3 x 3 x 5
Fa c t o r s ofa l e e b ra i c e x p r e s s
i o n s
Te r m s are fo r m e d as procluct of factors.
e.g. S•v = 5 x x x y
1Ox x+2 +3 —2x5xss x+2
x +3

4. ’îrreôuciÄÏe îaùÏars.”TÜen Ëa”ùe out ïËe
common factors of the terms and write the
remalning fact‹ors togetthe
desireBfactorform.
- E.g. Sab+10a
(5xaxb)+
(lOxa)
!
’)

5. Fa c t e r i s a t i n n b
• Regrouping is re-arra nging the terms with co m m on
terms.
2) 11:‹L - Ei.a + SL - 2
3 at5 b-2) + 1 ( 5 b 2)
(3ae1) (5b-2)

9. R e g r o u p i n g like t e r m s Ł e finch c o m m o n fac tors
lSpD v 9D v 2Sp mls
3q ( Bp + 3 ) + 5 ( Up + 3
)

10. Factorisation usin
- Observe the expression.
• If it has a form that fits the right hand side of one of the identities ,
then the
e•pressior› corresponding to the left hancl sicJe of the icJentity
gives the desir
e‹d fa ct or isation.
• (a-b)’ = a’-Zab+b’
- (V-& ) = (a+b)(a-b)

11. • *) •r+a•' +
as
tt is in the form o7tbe fclerrtity
a’+aab+bi
t h e r e t o
Sfr›co @"w 2wb a@= {a+lag
.
By comparison
p'. + at> -> xs e + 4/
{ re<tulred
factorisatton”)
. .

12. Factorise
• A9p“ — 3
6
(7'p)” — (6)“
(7p+6)(7p-6)
-a — 2 a b
+cb- — (a-bc)‘’ —
{a-b-c) (a-b+ c)

13. Factors of the
f o r m
x + b
• I n g e n e raI , for f actor isin g a n algebr aic ex pressi on of the
t y p e x + p x + q , w e fi n d
t w o fa ct ors a a ncl b of q (i .e. the con
stant
te r m ) such tha t
a b q
a +b p

15. 4o:* 8:x: -
+-
4(+2
4(æ2
in
4[x(x
in -e

17. n 2 7u 3u -I- Z
1
a a
ț 7) 3(n 7)

19. Œvłałon at wsonomłal by
another

23. ø
(zri
1.tSzri -+-Z.r»i 3Z)
[rzi(rzi 1 O) —+—
Z(zrı
1
O)]