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
Let us assume, if the given polynomial ( 2 x4 + 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 x4 + 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
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