Question

on dividing x^3-5x^2+14x-6 by a polynomial g(x),the quotation and the remainder are x-2 and 3x+4 ,find g(x)

Answer 1

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Answer 2

Hey dear!!!

Refer from the attachment which I have provided.

Explanation,

We have given that,

While diving p(x) = x³ - 5x² + 14x - 10 by g(x) the Quotient comes x - 2 and remainder as 3x + 4

We know the Euclid division algorithm which is ,

Dividend = Divisor x Quotient + Remainder

Here, we have ,

Dividend => x³ - 5x² + 14x - 6
Divisor ===> g(x)
Quotient => x - 2
Remainder => 3x + 4

Now, Simply putt the given value according to the formula, we get

x³ - 5x² + 14x - 6 = g(x) * (x-2) + 3x + 4

Now, take remainder left hand side from right hand side we get,

x³ - 5x² + 14x - 6 - 3x - 4 = g(x)* (x-2)

x³ - 5x² + 11x - 10 = g(x) *(x-2)

x³ - 5x² + 11x - 10/ x-2 = g(x)

Now, divide it,

Refer the attachment you will find the division of this,

The value of g(x) comes as [x² - 3x + 5]

Thanks !!!

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