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Give examples of polynomial p(x),q(x),r(x),g(x)which satisfy …

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Give examples of polynomial p(x),q(x),r(x),g(x)which satisfy the division algorithm and 1.deg p(x)=deg q(x), 2.deg q(x)=deg r(x),3.deg r(x)=0
  • 1 answers

Sia ? 6 years, 4 months ago

  1. deg p(x) = deg q(x)
    {tex}p ( x ) = 2 x ^ { 2 } - 2 x + 14{/tex}
    g(x) = 2
    q(x) = x2 - x + 7
    r(x) = 0
    Clearly, p(x) = q(x) {tex} \times {/tex} g(x) + r(x)
  2. deg q(x) = deg r(x)
    {tex}p ( x ) = x ^ { 3 } + x ^ { 2 } + x + 1{/tex}
    {tex}g ( x ) = x ^ { 2 } - 1{/tex}
    q(x) = x + 1
    r(x) = 2x + 2
    Clearly, {tex}p ( x ) = q ( x ) \times g ( x ) + r ( x ){/tex}
  3. deg r(x) = 0
    {tex}p ( x ) = x ^ { 3 } + 2 x ^ { 2 } - x - 2{/tex}
    {tex}g ( x ) = x ^ { 2 } - 1{/tex}
    q(x) = x + 2
    r(x) = 4
    Clearly, {tex}p ( x ) = q ( x ) \times g ( x ) + r ( x ){/tex}
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