Question

On dividing x3-3x2+x+2 by a polynomial g(x), the quotient and remainder were x–2 and –2x+4, respectively. Find g(x).
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Answer 1

Answer:

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Explanation:

November 1889 – 27 May 1964) was an Indian independence activist and, subsequently, the first Prime Minister of India, as well as a central figure in Indian politics both before and after independence. He emerged as an eminent leader of the Indian independence movement, serving India as Prime Minister from its establishment in 1947 as an independent nation, until his death in 1964. He was also known as Pandit Nehru

Answer 2

p(x) =x3-3x2+x+2

q(x) =x-2

r(x) = -2x +4

we know that, p(x) =g(x) ×q(x) +r(x)

x3-3x2+x+2=x-2×g(x)+(- 2x + 4)

g(x) =x3-3x2+x+2/x-2=x3-3x2+3x+2/x-2

x-2) x3-3x2+3x+2(x2-x+1

x3 -2x2

___________

-x-2+3x

-x2+2x

___________

x-2

x-2

therefore, g(x) =x2-x+1