If the polynomial 2x⁴ + x³ - 3x² +18x + 24 is divided by another polynomial x² + 3x - m and  the remainder comes out to be 4x + n. Find the value of m and n respectively.

Asked by Aasthaachd | 8th Jun, 2021, 01:39: PM

Expert Answer:

Let us assume, if the given polynomial ( 2 x + x3 - 3 x2 + 18x + 24 ) is divided by ( x2 + 3x - m ) ,
we get quotient ( a x2 + b x + c ) and remainder (4x+n) .
 
Then we have, ( a x2 + b x + c ) ( x2 + 3x - m ) + ( 4x + n ) = ( 2 x + x3 - 3 x2 + 18x + 24 ) 
 
LHS = a x4 + ( 3a + b ) x3 + ( 3b + c - a m ) x2 + ( 3 c - b m + 4) x - c m  + ( n - c m ) 
 
By comparing Coefficients , we get , a = 2 ,  ( 3a+b ) = 1 ,  ( 3b +c - a m ) = -3 ,
 
  ( 3c -bm ) =14  and ( n - c m ) = 24 
 
By solving these equations , we get m = -2 and n = 8

Answered by Thiyagarajan K | 20th Sep, 2021, 09:37: AM