Question

on dividing the polynomial 4 x^4 - 5 x cube - 39 x square - 6 x minus 2 by the polynomial g of x, the quotient and remainder when x square - 3 x - 5 and - 5 x + 8 respectively find g of x​

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KrishnaKant69

KrishnaKant69

20.04.2018

Math

Secondary School

+5 pts

Answered

On dividing the polynomial 4x^4-5x^3-39x^2-46x-2 by polynomial g(x), the quotient and remainder are x^2-3x-5 and -5x+8 respectively. Find g(x)

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siddhartharao77

siddhartharao77 Genius

Given polynomial p(x) = 4x^4 - 5x^3 - 39x^2 - 46x - 2.

Given Quotient q(x) = x^2 - 3x - 5

Given Remainder r(x) = -5x + 8.

We know that g(x) = p(x) - r(x)/q(x)

= 4x^4 - 5x^3 - 39x^2 - 46x - 2 - (-5x + 8)/x^2 - 3x - 5

= 4x^4 - 5x^3 - 39x^2 - 46x - 2 + 5x - 8/x^2 - 3x - 5

= 4x^4 - 5x^3 - 39x^2 - 41x - 10/x^2 - 3x - 5.

Now,

4x^2 + 7x + 2

-----------------------------------------------------

x^2 - 3x - 5) 4x^4 - 5x^3 - 39x^2 - 41x - 10

4x^4 - 12x^3 - 20x^2

-----------------------------------------------------------

7x^3 - 19x^2 - 41x

7x^3 - 21x^2 - 35x

---------------------------------------------------------------

2x^2 - 6x - 10

2x^2 - 6x - 10

--------------------------------------------------------------------

0.

Hence, g(x) = 4x^2 + 7x + 2.

Hope this helps!