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Dividing a Polynomial by a Monomial

Here, we divide each term of the polynomial of the
numerator by the monomial of the denominator. Get it right!
Example 11: Divide 16x − 12
2
l = 4x – 12
2
(a) 24(x yz + xy z + xyz ) by 8xyz 4x
2
2
16x − 12 44x − 3) 4x − 3 3
2
2
(
2
2
3 4
(b) 6ab – 16a b by –2ab 2 l 4x = 4x = x = 4x − x
Solution: (a) We have,
2
+
2
24(xyzxyz xyz 2 )
+
2
2
2
24(x yz + xy z + xyz ) by 8xyz =
8xyz
8 ×× xyz × xy z)
3
(
+ +
= 8 × xyz = 3(x + y + z)
(b) We have,
6ab − 16ab
3 4
2
6ab – 16a b by –2ab =
3 4
2
2
− 2ab 2
3 8ab )
2ab ( − 2 2
2
2 2
= = –(3 – 8a b ) = –3 + 8a b
2 2
− 2ab 2
Dividing a Polynomial by a Polynomial
In the division of a polynomial by a polynomial, we factorise both the polynomials and cancel
their common factors.
Example 12: Divide
(a) (2x + 8x) by (x + 4) (b) (x – 22x + 117) by (x – 13)
2
2
Solution: (a) We have,
(
2
2x + 8x 2xx + 4)
2
(2x + 8x) by (x + 4) = = = 2x
( x + 4) ( x + 4)
(b) We have,
2
2
−
x − 22 x 117 x − 13 x 9 x 117
+
+
(x – 22x + 117) by (x – 13) = =
2
−
−
( x 13) ( x 13)
xx ( − 13 ) − 9 x ( − 13 ) ( x − 13 ) x ( − 9 )
= = = (x – 9)
x ( − 13 ) x ( − 13 )
Example 13: Divide: 75abc(4a – 8)(5b – 15) by 125(a – 2)(b – 3).
Solution: We have
)(
75abca − 8 5b − 15)
4 (
75abc(4a – 8)(5b – 15) by 125(a – 2)(b – 3) =
)
(
(
125 a − 2 b − 3)
3
(
75 4×× 5 × abca − 2)(b − 3)
=
5
25 × (a − 2)(b − 3)
(
34 abca − 2) (b − 3)
××
= = 12abc
(a − 2) (b − 3)
305 Factorisation