Sol.
Dividend =
x4 – 5x + 6
Divisor =
2 – x2
x4
=
–x2
=
+
+ 0x3
+ 0x2
– 5x
+ 6
– 5x
x4
+ 6
2
Exercise 2.3
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and
remainder in each of the following :
1.
(iii) p(x) = x4 – 5x + 6, g(x) = 2 – x2
–
1
0
x
x2
2
–x2 + 2
x4 + 0x3 + 0x2 – 5x + 6
(–)
x4
(+)
2x2
– 5x + 6
– 2
+
(–)
– 5x
– 2x2
2x2 – 4
+ 10
+
(+)
Quotient =
Remainder =
x2 + 2
– 5x + 10
∴
x4
–x2
=
–x2
(–x2 + 2)
x4
–
2x2
=
2x2
–x2
=
–2
(–x2 + 2)
2x2
–
4
–2
=
2
–x2
–x2
–
–
+
–
–
+
1
2