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

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To find the polynomial P(x), use the formula P = AQ + R, where A is the divisor (2x + 1), Q is the quotient (x^2 - x + 2), and R is the remainder (5). Substitute these values into the equation to get P(x) = (2x + 1)(x^2 - x + 2) + 5. Expand the product and simplify to derive the complete polynomial. The final result will provide the expression for P(x). This method effectively utilizes the relationship between polynomials, quotients, and remainders.
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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