Question

find tge remainder of 3x³-10x²+6x-1 which is divided by x-1, using remainder theorem​

Answer 1

SOLUTION

TO DETERMINE

The remainder of 3x³-10x²+6x-1 which is divided by x-1, using remainder theorem

EVALUATION

Let f(x) = x - 1

$\sf{g(x) = 3 {x}^{3} - 10 {x}^{2} + 6x - 1 }$

For Zero of the polynomial f(x) we have

$\sf{f(x) = 0}$

$\implies \sf{x - 1 = 0}$

$\implies \sf{x = 1 }$

So by Remainder Theorem the required Remainder when g(x) is divided by f(x) is

$\sf{ = g(1) }$

$\sf{ = 3 \times {(1)}^{3} - 10 \times {(1)}^{2} + 6 \times 1 - 1 }$

$\sf{ = 3 - 10 + 6 - 1 }$

$= - 2$

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