Sol.
Exercise 2.3
Give examples of polynomials p(x), g(x), q(x) and r(x)
which satisfy the division algorithm and
1.
(i) deg p(x) = deg q(x)
p(x)
=
2x²
–
2x
+
14,
g(x)
=
2
q(x)
=
x²
–
x
+
7,
r(x)
=
0
Dividend = Divisor × Quotient + Remainder
–
x
+
7
2ge2
–
–
2x
+
14
–
2x
+
14
14
(–)
0
2
2x2 – 2x + 14
x2
2
2
2
–
x
+
7
x2
0
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
Sol.
Exercise 2.3
Give examples of polynomials p(x), g(x), q(x) and r(x)
which satisfy the division algorithm and
1.
(i) deg p(x) = deg q(x)
p(x)
=
2x²
–
2x
+
14,
g(x)
=
2
q(x)
=
x²
–
x
+
7,
r(x)
=
0
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
(ii) deg q(x) = deg r(x)
x
+
1
x3
–
x
(–)
(+)
x2
+
2x
+
1
x2
–
1
(–)
(+)
2x
+
2
x3 + x2 + x + 1
x² – 1
2x
+
2
1
x² – 1
x
+
1
x3 + x2 + x + 1
p(x)
=
x³
+
x²
+
x
+
1,
g(x)
=
x²
–
1
q(x)
=
x
+
1,
r(x)
=
2x
+
2
1
Sol.
Exercise 2.3
Give examples of polynomials p(x), g(x), q(x) and r(x)
which satisfy the division algorithm and
1.
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
(iii) deg r(x) = 0
x2
+
1
x3
+
2x2
(–)
(–)
x
+
2
x
+
2
(–)
(–)
0
x3 + 2x2 + x + 2
x + 2
x3 + 2x2 + x + 2
x + 2
x2
+
1
0
=
p(x)
x³
+
2x²
+
x
+
2,
q(x)
=
x²
+
1
=
g(x)
x
+
2,
r(x)
=
0
(ii) deg q(x) = deg r(x)
p(x)
=
x³
+
x²
+
x
+
1,
g(x)
=
x²
–
1
q(x)
=
x
+
1,
r(x)
=
2x
+
2