IF a x cubed space plus space b x to the power of 2 space end exponent space plus space x minus 6 space space H A S space x plus 2 space A S space A space F A C T O R space A N D space L E A V E S space A space R E M A I N D E R space 4 space W H E N space D I V I D E D space B Y space space x minus 2 space space F I N D space T H E space V A L U E space O F A space & space B space ?

Asked by Sunny | 3rd Jun, 2017, 12:03: PM

Expert Answer:

begin mathsize 14px style Let space straight p left parenthesis straight x right parenthesis equals ax cubed plus bx squared plus straight x minus 6
Since space left parenthesis straight x plus 2 right parenthesis space is space straight a space factor space of space straight p left parenthesis straight x right parenthesis comma
straight p left parenthesis 2 right parenthesis equals 0
rightwards double arrow straight a left parenthesis negative 2 right parenthesis cubed plus straight b left parenthesis negative 2 right parenthesis squared minus 2 minus 6 equals 0
rightwards double arrow negative 8 straight a plus 4 straight b minus 8 equals 0
rightwards double arrow negative 2 straight a plus straight b minus 2 equals 0
rightwards double arrow negative 2 straight a plus straight b equals 2 space space space space space space space space space space.... left parenthesis 1 right parenthesis
It space is space given space that space straight p left parenthesis straight x right parenthesis space leaves space remainder space 4 space when space it space is space divided space by space left parenthesis straight x minus 2 right parenthesis
rightwards double arrow straight p left parenthesis 2 right parenthesis equals 4
rightwards double arrow straight a left parenthesis 2 right parenthesis cubed plus straight b left parenthesis 2 right parenthesis squared plus 2 minus 6 equals 4
rightwards double arrow 8 straight a plus 4 straight b minus 4 equals 4
rightwards double arrow 2 straight a plus straight b minus 1 equals 1
rightwards double arrow 2 straight a plus straight b equals 2 space space space space space space space space space space.... left parenthesis 2 right parenthesis
Adding space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get
2 straight b equals 4
rightwards double arrow straight b equals 2
Substituting space straight b equals 2 space in space left parenthesis 2 right parenthesis comma space we space get
2 straight a plus 2 equals 2
rightwards double arrow 2 straight a equals 0
rightwards double arrow straight a equals 0
Hence comma space straight a equals 0 space and space straight b equals 2 end style

Answered by Rashmi Khot | 3rd Jun, 2017, 09:13: PM