Question

Show that (x+3) is a factor of p(x) =69+11x-x²+x³.

Answer 1

Let p( x ) = x³ - x² + 11x + 69

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By Factor theorem :

If p( a ) = 0 then ( x - a ) is a factor of

p( x ).

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p( -3 ) = ( - 3 )³ - ( -3 )² + 11( -3 ) + 69

= -27 - 9 - 33 + 69

= -69 + 69

= 0

p ( -3 ) = 0

Therefore ,

( x - 3 ) is a factor of p( x ).