Math, asked by ramchaudhary2112005, 6 hours ago

on dividing x3 - 3x2 +x + 2 by a polynomial g(x) the quotient and reminder were x - 2 and -2 + 4 respectively. find g(x)​

Answers

Answered by RvChaudharY50
1

Given :- On dividing x³ - 3x² + x + 2 by a polynomial g(x) the quotient and reminder were x - 2 and -2x + 4 respectively. find g(x) = ?

Solution :-

we have,

→ Dividend = x³- 3x² + x + 2

→ Divisor = g(x)

→ Quotient = (x - 2)

→ Remainder = (-2x + 4)

we know that,

  • Dividend = Divisor * Quotient + Remainder

putting values we get,

→ x³- 3x² + x + 2 = g(x) * (x - 2) + (-2x + 4)

→ x³- 3x²+ x + 2 - 4 + 2x = g(x) * (x - 2)

→ x³ - 3x² + 3x - 2 = g(x) * (x - 2)

→ x³ - 3x² + 2x + x - 2 = g(x) * (x - 2)

→ x(x² - 3x + 2) + x - 2 = g(x) * (x - 2)

→ x(x² - 2x - x + 2) + x - 2 = g(x) * (x - 2)

→ x[x(x - 2) - 1(x - 2)] + (x - 2) = g(x) * (x - 2)

→ x[(x - 2)(x - 1)] + (x - 2) = g(x) * (x - 2)

→ (x - 2)[x(x - 1) + 1] = g(x) * (x - 2)

→ x(x - 1) + 1 = g(x)

→ (x² - x + 1) = g(x)

therefore,

→ g(x) = (x² - x + 1) (Ans.)

Learn more :-

JEE mains Question :-

https://brainly.in/question/22246812

. Find all the zeroes of the polynomial x4

– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

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