Question

Find the remainder when x3+x2+3x+1 is divided by x -1/2
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Answer 1

$Find \: the \: remainder \: when \\ \: {x}^{3} + {x}^{2} +3x+1 \: is \: divided \: by \: x - \frac{1}{2} \\ \\ solution. \\ x - \frac{1}{2} = 0 \\ x = \frac{1}{2} \\ \\ p(x) = {x}^{3} + {x}^{2} +3x+1 \\ \\ p( \frac{1}{2} ) = {( \frac{1}{2} )}^{3} + {( \frac{1}{2} )}^{2} + 3( \frac{1}{2} ) + 1 \\ \\ = \frac{1}{8} + \frac{1}{4} + \frac{3}{2} + 1 \\ \\ = \frac{1 + 2 + 12 + 8}{8} \\ \\ = \frac{23}{8} \: \: \: remainder...$