What is the Polynomial P(x) Given a Specific Quotient and Remainder?

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SUMMARY

The polynomial P(x) can be determined using the division algorithm for polynomials. Given that P(x) is divided by (2x + 1) with a quotient of (x^2 - x + 2) and a remainder of 5, the formula P(x) = (2x + 1)(x^2 - x + 2) + 5 can be applied. After performing the multiplication and simplification, P(x) is found to be 2x^3 - x^2 + 4x + 7. This method effectively utilizes the relationship between the divisor, quotient, and remainder to reconstruct the original polynomial.

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Students in algebra, mathematics educators, and anyone interested in polynomial functions and their properties will benefit from this discussion.

missnerdist
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I can't seem to figure this out.

When a polynomial P(x) is divided by (2x+1) the quotient is x^2-x+2 and the remainder is 5. What is P(x)?
 
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A hint: When 7 is divided by 3 the quotient is 2 and the remainder is 1.
 
If P divided by A has quotient Q with remainder R, P/A= Q+ R/A, then P= AQ+ R. You are told what A, Q, and R are. Just do the algebra to find P.
 

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