Give example of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm

Give example of polynomial p(x), g(x), q(x) and r(x), which satisfy th

1.	Give example of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm
Answer» \tdeg p(x) = deg q(x)\t{tex}p ( x ) = 2 x ^ { 2 } - 2 x + 14{/tex}\tg(x) = 2\tq(x) = x2 - x + 7\tr(x) = 0\tClearly, p(x) = q(x) {tex} \\times {/tex}\xa0g(x) + r(x)\tdeg q(x) = deg r(x)\t{tex}p ( x ) = x ^ { 3 } + x ^ { 2 } + x + 1{/tex}\t{tex}g ( x ) = x ^ { 2 } - 1{/tex}\tq(x) = x + 1\tr(x) = 2x + 2\tClearly,\xa0{tex}p ( x ) = q ( x ) \\times g ( x ) + r ( x ){/tex}\tdeg r(x) = 0\t{tex}p ( x ) = x ^ { 3 } + 2 x ^ { 2 } - x - 2{/tex}\t{tex}g ( x ) = x ^ { 2 } - 1{/tex}\tq(x) = x + 2\tr(x) = 4\tClearly,\xa0{tex}p ( x ) = q ( x ) \\times g ( x ) + r ( x ){/tex}