Question : Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg q(x) = 0
Solution :
(i) Let q(x) = \(3x^2 + 2x + 6\), Degree of q(x) = 2
p(x) = \(12x^2 + 8x + 24\), Degree of p(x) = 2
Here, deg p(x) = deg q(x)
(ii) Let p(x) = \(x^5 + 2x^4 + 3x^3 + 5x^2 + 2\),
q(x) = \(x^2 + x + 1\), Degree of q(x) = 2
g(x) = \(x^3 + x^2 + x + 1\)
r(x) = \(2x^2 – 2x + 1\), Degree of r(x) = 2
Here, deg q(x) = deg r(x)
(iii) Let p(x) = \(2x^4 + 8x^3 + 6x^2 + 4x + 12\),
q(x) = 2, Degree of q(x) = 0
g(x) = \(x^4 + 4x^3 + 3x^2 + 2x + 1\)
r(x) = 10
Here, deg q(x) = 0
