SOLUTION: When a polynomial f(x) is divided by x-3 the remainder is -9 and when divided by 2x-1 the remainder is -6.Find the remainder when f(x) is divided by(x-3)(2x-1)
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Question 1135670: When a polynomial f(x) is divided by x-3 the remainder is -9 and when divided by 2x-1 the remainder is -6.Find the remainder when f(x) is divided by(x-3)(2x-1)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
When a polynomial is divided by the remainder is
=>
=>
and when divided by the remainder is
=>
=>
We want the remainder when is divided by .
So let , where is the quotient and is the remainder.
Being the remainder on division by a quadratic, must be a linear polynomial, say
.
So
means .....eq.1
means , or .....eq.2
Solve the system
.....eq.1
.....eq.2
----------------------------
.....eq.1.....solve for
......substitute that into eq.2
.....eq.2
......substitute
Conclusion: the remainder is
....substitute and
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
For three linear binomials and three remainders see the lesson
- Solved problems on the Remainder theorem, Problem 7.
in this site . . .
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