Question

On dividing the polynomial p of x is equal to 5 x power 4 minus 4 x power 3 + 3 x square - 2 x + 1 by another polynomial gfx is equal to x square + 2 if the quotient is x square + bx + c find a b and c

Answer 1

x^2+2)5x^4-4x^3+3x^2-2x+1(5x^2-4x-7
5x^4. +10x^2
____________
-4x^3-7x^2
-4x^3-8x
______________
-7x^2+6x
-7x^2-14
_______________
6x-13


a=5,b=-4,c=-7

Answer 2

Answer:

Value of a is 5 , b is -4 and c is -7.

Step-by-step explanation:

Given:

Dividend = p(x) = $5x^4-4x^3+3x^2-2x+1$

Divisor = g(x) = $x^2+2$

On division Quotient we get = $ax^2+bx+c$

To find: Value of a , b and c.

We divide both polynomial by long division method and compare the obtained quotient with given quotient.

then find value of a , b and c

Long Division is attached in pic.

We obtained,

Quotient = 5x² - 4x - 7

Remainder = 6x + 15

So, On comparing

a = 5 , b = -4 and c = -7

Therefore, Value of a is 5 , b is -4 and c is -7.