Question

On dividing x^3-8x^2+20x-10 by polynomial g(x), the quotient and the reminder were x-4 and 6 respectively. find g(x)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept

Polynomial consists of variables and their coefficients so that it can express the values of variables. It is in not in equal to form.

Given

Polynomial and divident is $x^{3} -8x^{2} +20x-10$

To find

The polynomial which divides polynomial $x^{3} -8x^{2} +20x-10$ gives quotient x-4 and remainder 6.

Explanation

let the polynomial which when divides  polynomial $x^{3} -8x^{2} +20x-10$ gives quotient x-4 and remainder 6 be y.

and we know that Divident =Divisor*quotient +remainder

In the given question divident is polynomial $x^{3} -8x^{2} +20x-10$ . quotient is x-4 and remainder is 6.

$x^{3} -8x^{2} +20x-10$=y*(x-4)+6

$x^{3} -8x^{2} +20x-10$-6=y(x-4)

$x^{3} -8x^{2} +20x-16$=y(x-4)

$(x^{3} -8x^{2} +20x-16)/(x-4)$=y

y=$x^{2} -4x+4$

Hence the polynomial is $x^{2} -4x+4$ which when divides the given polynomial gives quotient x-4 and remainder 6.

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