what must be added to p(x)=4x 4 +2x 3 -2x 2 +x-1 so that the resulting polynomial is divisible by g(x)=x 2 +2x-3
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P(x ) = 4x⁴ +2x³ -2x² +x -1
let g(x ) is unknown polynomial , such that
P(x ) + g(x ) = x² +2x -3
4x⁴ + 2x³ -2x² +x -1 + g(x)= x² +2x -3
g(x) = (x² +2x -3) -(4x⁴+2x³ -2x² +x -1)
= -4x⁴ +3x² -2 -2x³ + x
=-4x⁴ -2x³ +3x² + x -2
let g(x ) is unknown polynomial , such that
P(x ) + g(x ) = x² +2x -3
4x⁴ + 2x³ -2x² +x -1 + g(x)= x² +2x -3
g(x) = (x² +2x -3) -(4x⁴+2x³ -2x² +x -1)
= -4x⁴ +3x² -2 -2x³ + x
=-4x⁴ -2x³ +3x² + x -2
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