SOLUTION: When f(x)= ax^2+bx-4 is divided by x+2, the remainder is -2. When f(x) is divided by x+3, the remainder is 5. Find the values of a and b.
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Question 1018703: When f(x)= ax^2+bx-4 is divided by x+2, the remainder is -2. When f(x) is divided by x+3, the remainder is 5. Find the values of a and b.
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
The first part means that .
The second part means that .
The question's solution is based on use of the Remainder and Factor Theorems. You do not actually need to perform the divisions because the factor & remainder theorems tell you that those results are expected to work; so just solve a system of two equations in two unknowns, being unknowns a and b.
Review how the Remainder & Factor Theorems work.
Substitute the needed values for x to get this system:
Simplify the system:
Solve for a and b. The steps for this are not included here.
----You must already know how to correctly solve such a system as expected according your course level being COLLEGE ALGEBRA.
The function you should find is .
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