Question

14.Give an example of polynomials f(x), g(x), q(x) and r(x ) satisfying f(x) = g(x).q(x) + r(x) where degree { r(x) } = 0

Standard:- 10

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Answer 1

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HERE IS YOUR ANSWER,

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Using division algorithm, we have

$f(x) = g(x) \times q(x) + r(x)$


${x}^{5} - 4 {x}^{3} + {x}^{2} + 3x + 1 = ( {x}^{3} - 3x + 1)( {x}^{2} - 1) + 2 \\ \\ {x}^{5} - {4x}^{3} + {x}^{2} + 3x + 1 = {x}^{5} - 3 {x}^{3} + {x}^{2} - {x}^{3} + 3x - 1 + 2 \\ \\ {x}^{5} - 4 {x}^{3} + {x}^{2} + 3x + 1 = {x}^{5} - 3 {x}^{3} - {x}^{3} + {x}^{2} + 3x - 1 + 2 \\ \\ {x}^{5} - 4 {x}^{3} + {x}^{2} + 3x + 1 = {x}^{5} - 4 {x}^{3} + {x}^{2} + 3x + 1$




Hence an example for polynomial f(x) , g(x), q(x) and r(x) satisfying  f(x) = g(x) × q(x) + r(x) are


$f(x) = {x}^{5} - 4 {x}^{3} + {x}^{2} + 3x + 1 \\ \\ g(x) = ( {x}^{3} - 3x + 1) \\ \\ q(x) = ({x}^{2} - 1) \\ \\ r(x) = 2$


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# Nikky