Posted by T.Gracken on October 25, 2002 at 12:57:27:
In Reply to: equation posted by Jerry on October 25, 2002 at 12:03:33:
: When ax^3-x^2-x+b is divided by x-1, the remainder is 6.
: When it is divided by x+2, the remainder is 9.
: What are a and b?
: Doesn't seem possible to solve. Help please.
certainly it does! but you have to use the remainder thereom for it to make sense.
that is, if f is a polynomial function divided by (x-k), then f(k) is the remainder.
so if the remainder is 6 when dividing by (x-1), then replace the x's in ax^3-x^2-x+b with 1 and it must equal 6
that is... a-1-1+b=6
or a + b = 8.
do the same for the other given information; that is if divide by (x+2) the remainder is 9. note that x+2= x-(-2), so replace x's with -2 and we get
or -8a + b = 11
now you have two equations with two unknowns, solve for a and b.
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