Question

divide the polynomial x^3 - 2x^2+4x -18 by polynomial (x-3) abd verify division algorithm theorom

Please answer fast...

Answer 1

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Answer 2

Answer:

$q(x) = x^2 + x + 7\\\\r(x) = 3$

Step-by-step explanation:

Here,

$p(x) = x^3 - 2x^2 + 4x - 18\\\\g(x) = x -3$

On dividing p(x) by g(x) (For the division process, refer to the attachment), we get:

$q(x) = x^2 + x + 7\\\\r(x) = 3$

We know that

$p(x) = g(x) \times q(x) + r(x)\\\\LHS = x^3 - 2x^2 + 4x - 18\\\\RHS = (x-3)(x^2 + x + 7) + 3\\\\= x^3 + x^2 + 7x - 3x^2 - 3x - 21 + 3\\\\= x^3 - 2x^2 + 4x - 18\\\\LHS = RHS$

Hence proved!