3
Question
Show that (x+3) is a factor of p(x) =69+11x-x²+x³.
Show that (x+3) is a factor of p(x) =69+11x-x²+x³.
Open in App
Solution
Let p( x ) = x³ - x² + 11x + 69
*****************************
By Factor theorem :
If p( a ) = 0 then ( x - a ) is a factor of
p( x ).
********************************
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 ).
*****************************
By Factor theorem :
If p( a ) = 0 then ( x - a ) is a factor of
p( x ).
********************************
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 ).
Suggest Corrections
40
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
