SOLUTION: The expression 8x^3 + ax^2 + bx - 9 leaves remainders -95 and 3 when divided by x + 2 and 2x - 3 respectively. Calculate the value of a and of b.

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Question 1183387: The expression 8x^3 + ax^2 + bx - 9 leaves remainders -95 and 3 when divided by x + 2 and 2x - 3 respectively. Calculate the value of a and of b.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!



given:

is a factor of given polynomial


Remainder =
is a factor of given polynomial



Remainder =

..........Put the value of



...........solve for

...........eq.1






.......both sides multiply by
.......simplify
.......solve for

...........eq.2

from eq.1 and eq.2
......solve for




go to
...........eq.1, substitute
...........eq.1


then your expression is:



check reminders:







Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

The expression 8x^3 + ax^2 + bx - 9 leaves remainders -95 and 3 when divided by x + 2 and 2x - 3 respectively. Calculate the value of a and of b.
As usual, if you ant to "TORTURE" yourself, then go along with that CONFUSING, TIME-CONSUMING, 
and UNNECESSARY PARTIAL-setup by that woman who responded,


With remainder from factor x + 2 being - 95, we see that x + 2 = 0 ===> x = - 2, which means that: 
                                                                                                                                 
                                                                         
With remainder from factor 2x - 3 being 3, we see that 2x - 3 = 0 ===> x = , which means that: 
                                                                        
                                                                         
     - 22 =  4a - 2b --- eq (i)
     - 60 =  9a + 6b --- eq (ii)
     - 66 = 12a - 6b --- Multiplying eq (i) by 3 ------ eq (iii)
    - 126 = 21a -------- Adding eqs (ii) & (iii)
 

     - 22 = 4(- 6) - 2b ----- Substituting - 6 for a in eq (i)
     - 22 = - 24 - 2b
- 22 + 24 = - 2b
        2 = - 2b

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