A polynomial p(x) divided by x² − 2x + 1 gives the quotient x + 3 and the remainder 4x − 2. Then p(x) is:

Question

Accepted Answer

x³ + x² − x + 1. By the division algorithm, p(x) = divisor × quotient + remainder = (x² − 2x + 1)(x + 3) + (4x − 2). Now (x² − 2x + 1)(x + 3) = x³ + x² − 5x + 3, and adding 4x − 2 gives x³ + x² − x + 1. (Stopping before adding the remainder gives the first option.)

A polynomial p $(x)$ divided by $x^{2} - 2 x + 1$ gives the quotient $x + 3$ and the remainder $4 x - 2$ . Then p $(x)$ is:

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More Algebra practice

A polynomial p(x) divided by x2−2x+1 gives the quotient x+3 and the remainder 4x−2. Then p(x) is:

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

A polynomial p $(x)$ divided by $x^{2} - 2 x + 1$ gives the quotient $x + 3$ and the remainder $4 x - 2$ . Then p $(x)$ is: