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

a)  a   = - ( 5 + b ) / 9

b) no remainder

Step-by-step 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

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)