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.

Algebra ->  Polynomials-and-rational-expressions -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The first part means that f%28-2%29=-2.

The second part means that f%28-3%29=5.

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:
system%28a%2A%28-2%29%5E2%2Bb%2A%28-2%29-4=-2%2Ca%2A%28-3%29%5E2%2Bb%2A%28-3%29-4=5%29

Simplify the system:
system%284a-2b=2%2C9a-3b=9%29
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 highlight%28f%28x%29=2x%5E2%2B3x-4%29.