SOLUTION: Given that (x+3) and (x-1) are both factors of the same expression x^3+ax^2-bx-a,find the values of the constants a and b. Determine the third factor or the expression.

Question 175202: Given that (x+3) and (x-1) are both factors of the same expression x^3+ax^2-bx-a,find the values of the constants a and b.
Determine the third factor or the expression.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given that (x+3) and (x-1) are both factors of the same expression x^3+ax^2-bx-a,find the values of the constants a and b.
Determine the third factor or the expression.
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If x-1 is a factor, f(1) = 0
f(1) = 1^3 + a(1^2) - b(1) -a = 1 + a -b -a = 1-b = 0
Therefore b = 1
-------------------------
If x+3 is a factor, f(-3) = 0
f(-3) = (-3)^3 + a(-3)^2 - b(-3) -a = 0
-27 + 9a +3b -a = 0
Substitute b=1 and get
-27 +8a + 3 = 0
8a = 24
a = 3
===========
f(x) = x^3+ax^2-bx-a
f(x) = x^3 + 3x^2 -x - 3
-----------------------
Use synthetic division to find the 3rd factor:
1)....1....3....-1....-3
.......1......4...3...|..0
-3).....1......1..|..0
3rd factor: x + 1
=========================
Cheers,
Stan H.

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