Factorisation is the reverse of multiplication. Factorise 15; we get factors 3 and 5.

**Factorisation**

Factorisation
is the reverse of multiplication.

For Example : Multiply
3 and 5; we get product 15.

Factorise
15; we get factors 3 and 5.

For Example : Multiply
(*x* + 2) and (*x* + 3); we get product *x* ^{2} +
5*x* + 6 .

Factorise
*x* ^{2} + 5*x* +
6 ; we get factors (*x* + 2) and (*x* + 3).

Thus, the
process of converting the given higher degree polynomial as the product of factors
of its lower degree, which cannot be further factorised is called factorisation.

**Two important ways of factorisation are :**

(i)
By taking common factor

*ab +ac*

*a × b + a × c*

*a (b +c)* factored form

(ii)
By grouping them

*a + b − pa − pb*

(a
+* b *) − *p(*a +b) group in pairs

(a
+* b *)(1 − p) factored form

When
a polynomial is factored, we “factored out” the common factor.

**Example 3.24**

Factorise
the following:

(i)
*am* + *bm* +*cm* (ii) *a* ^{3} − *a*^{2}*b* (iii)
5*a* − 10*b* − 4*bc* +
2*ac* (iv) *x* + *y* −1
–*xy*

*Solutions*

(i)
*am* + *bm* +*cm*

*am
*+*
bm *+*cm*

*m
*(*a *+*
b *+*c*)* *factored form

(ii)
*a* ^{3} − *a*^{2}*b*

* a *^{2}* *⋅* a *− *a
*^{2}* *⋅*b *group in pairs

* a *^{2}* *×* *(*a *−*b*)* *factored form

(iii)
5*a* − 10*b* − 4*bc* +
2*ac*

5*a*
−
10*b* + 2*ac* − 4*bc*

5(*a*
−
2*b*) + 2*c*(*a* −2*b*)

(*a*
−
2*b* )(5 + 2*c*)

(iv)
*x* + *y* −1 −*xy*

*x
*−*
*1* *+*y
*–*xy*

(*x*
−
1) +*y*(1 −*x*)

(*x*
− 1) -*y*(*x* -1)

(*x*
− 1)(1 -*y*)

(*a* − *b* ) = − (*b-a*)

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9th Maths : UNIT 3 : Algebra : Factorisation | Explanation, Example Solved Problems | Algebra | Maths

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