Question<\/strong> : Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and<\/p>\n
(i)<\/strong>\u00a0 deg p(x) = deg q(x)<\/p>\n
(ii)<\/strong>\u00a0 deg q(x) = deg r(x)<\/p>\n
(iii)<\/strong>\u00a0 deg q(x) = 0<\/p>\n
Solution<\/strong> :<\/p>\n
(i)<\/strong>\u00a0 Let q(x) = \\(3x^2 + 2x + 6\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) = 2<\/p>\n
p(x) = \\(12x^2 + 8x + 24\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of p(x) = 2<\/p>\n
Here, deg p(x) = deg q(x)<\/strong><\/p>\n
(ii)<\/strong>\u00a0 Let p(x) = \\(x^5 + 2x^4 + 3x^3 + 5x^2 + 2\\),<\/p>\n
q(x) = \\(x^2 + x + 1\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) = 2<\/p>\n
g(x) = \\(x^3 + x^2 + x + 1\\)<\/p>\n
r(x) = \\(2x^2 – 2x + 1\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of r(x) = 2<\/p>\n
Here, deg q(x) = deg r(x)<\/strong><\/p>\n
(iii)<\/strong>\u00a0 Let p(x) = \\(2x^4 + 8x^3 + 6x^2 + 4x + 12\\),<\/p>\n
q(x) = 2,\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) = 0<\/p>\n
g(x) = \\(x^4 + 4x^3 + 3x^2 + 2x + 1\\)<\/p>\n
r(x) = 10<\/p>\n
Here, deg q(x) = 0<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"
Question : Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i)\u00a0 deg p(x) = deg q(x) (ii)\u00a0 deg q(x) = deg r(x) (iii)\u00a0 deg q(x) = 0 Solution : (i)\u00a0 Let q(x) = \\(3x^2 + 2x + 6\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) …<\/p>\n