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)
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):
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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
