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When ax3+bx-6 is divided by x+3,the remainder is 9. Find term of a only . The remainder when 2x3-bx2+2ax-4 when it is divided by x-2

User Sanghyun
by
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1 Answer

16 votes
16 votes

Answer:

a) a = - ( 5 + b ) / 9

b) no remainder

Explanation:

A) ( ax^3 + bx -6 ) / ( x + 3 )

Remainder = 9

determine the value of a

we will use the result of if ( x + a ) divides polynomial g(x) the remainder is g(a)

therefore given that ( x + 3 ) divides f(x) = ax^3 + bx - 6

= f( -3 ) = 9

= a(- 27 ) - 3b - 6 = 9

= -27a = 9 + 6 + 3b

therefore the term 'a' = - ( 15 / 27 + 3b / 27 )

= - ( 5/9 + b/9 )

a = - ( 5 + b ) / 9

b) Find the remainder when (2x^3 - bx^2 + 2ax - 4 ) is divided by (x-2 )

given that ( x -2 ) divides f(x) = 2x^3 - bx^2 + 2ax - 4

also given a = - ( 5 + b ) / 9 from previous polynomial above

= f(2) = ?

= 2(8) -4b + 4a - 4

= 16 - 4b + 4 ( - ( 5 + b ) / 9 ) - 4

= 16 - 4b + (( -20 - 4b ) / 9) - 4

= 16 - 4b - ( 20 - 4b ) / 9) - 4

= 16 - ( 32b - 20 ) / 9) - 4 = ?

therefore the remainder 'b' = ( -108 + 20 ) / 32 = - 2 3/4

since the remainder is negative there is no remainder then

User FelikZ
by
2.6k points
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