When x^2 - 8x + a is divided by x - 2, the remainder is 1, what is the remainder when it is divided by x - 1

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justaguide | College Teacher | (Level 2) Distinguished Educator

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If a polynomial P(x) is divided by x - a the remainder is P(a).

When x^2 - 8x + a is divided by x - 2, the remainder is 2^2 - 8*2 + a = -12 + a. This is equal to 1

-12 + a = 1

a = 13

The remainder when x^2 - 8x + 13 is divided by x - 1 is 1 - 8 + 13 = 6

The remainder when the given polynomial is divided by (x - 1) is 6

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