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 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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