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8. By Remainder Theorem find the remainder, when p(x) is divided by g(x), where
O P(x) = x-2 -4-1, 8(x) = x + 1
(i) P(x) = x - 3x² + 4x + 50. g(x)=x-3​

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king192005

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The remainder of P(x) = x - 3x² + 4x + 50  ÷  g(x)=x-3​ is 38.

Remainder theorem

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

Given to us

P(x) = x - 3x² + 4x + 50 \g(x)=x-3​

To find

P(x) = x - 3x² + 4x + 50  ÷  g(x)=x-3​

Solution

We know that the remainder of function P(x) ÷ g(x) according to the remainder theorem will be equal to P(3).

therefore,

[tex]P(x) = x -3x^2+ 4x + 50\\ P(x) = -3x^2+4x+x+50\\ P(x) = -3x^2+5x+50\\\\ P(3) = -3(3^2) +5(3) +50\\ P(3) = -3(9) + 15 +50\\ P(3) = -27 +15+50\\ P(3) = 38 [/tex]

Therefore, the remainder of P(x) = x - 3x² + 4x + 50  ÷  g(x)=x-3​ is 38.

Learn more about Remainder theorem:

https://brainly.com/question/4515216

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