Find the remainder when the polynomial (3x^3 - 5x^2 + 2x - 7) is divided by the binomial (x - 2).

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Accepted Answer

Step:1 ：(3x^3 - 5x^2 + 2x - 7 = (x - 2)Q(x) + R(x)), where (Q(x)) is the quotient and (R(x)) is the remainder.Step:2 ：Substitute the value of (x = 2) into the polynomial equation:    (3(2)^3 - 5(2)^2 + 2(2) - 7 = 2Q(2) + R(2)).    Simplify to get: (24 - 20 + 4 - 7 = 2Q(2) + R(2)), or (1 = 2Q(2) + R(2)).Step:3 ：Since (x - 2 = 0) when (x = 2), the remainder (R(x) = R(2) = 1 - 2Q(2)). But the remainder must be a constant, so (Q(2) = 0) and (R(2) = 1).

Answer

Step: 1 ：(3x^3 - 5x^2 + 2x - 7 = (x - 2)Q(x) + R(x)), where (Q(x)) is the quotient and (R(x)) is the remainder.Step: 2 ：Substitute the value of (x = 2) into the polynomial equation:    (3(2)^3 - 5(2)^2 + 2(2) - 7 = 2Q(2) + R(2)).    Simplify to get: (24 - 20 + 4 - 7 = 2Q(2) + R(2)), or (1 = 2Q(2) + R(2)).Step: 3 ：Since (x - 2 = 0) when (x = 2), the remainder (R(x) = R(2) = 1 - 2Q(2)). But the remainder must be a constant, so (Q(2) = 0) and (R(2) = 1).

Find the remainder when the polynomial \(3x^3 - 5x^2 + 2x - 7\) is divided by the binomial \(x - 2\).

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