Question

Divide 3x⁴+5x³-7x²+2x+2 by x²+3x+1, and verify the divison algorithm.

Step-by-step explain it
follow me also for follow back​

Answer 1

p(x) = 3x⁴+ 5x³- 7x² + 2x + 2

g(x) = x² + 3x + 1

r(x) = 0

q(x) = 3x² - 4x + 2

(refer attachment for division)

______________________

Division Algorithm = p(x) = g(x).q(x) + r(x)

______________________

Verification using division algorithm :-

p(x) = ( x²+3x+1 ) ( 3x² - 4x + 2 )

= 3x⁴ - 4x³ + 2x² + 9x³ - 12x² + 6x + 3x² - 4x + 2 + 0

= 3x⁴ + 5x³ - 7x²+ 2x + 2

Hence verified.

Answer 2

What is

`GIVEN :

The expression 3x^4+5x^3-7x^2+2x+2 divided by x^2+3x+1

TO FIND :

The quotient for the given expression by using Long Division Method.

SOLUTION :

Given that 3x^4+5x^3-7x^2+2x+2 divided by x^2+3x+1

Here by using the Long Division Method we have to find the quotient.

3x^2-4x+2

_________________________

x^2+3x+1 ) 3x^4+5x^3-7x^2+2x+2

3x^4+9x^3+3x2

_(-)__(-)___(-)_________

-4x^3-10x^2+2x

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

___(+)___(+)___(+)______

2x^2+6x+2

2x^2+6x+2

__(-)___(-)___(-)_______

0

__________________

Therefore the quotient when the given expression 3x^4+5x^3-7x^2+2x+2 divided by x^2+3x+1 is 3x^2-4x+2

∴ the quotient is 3x^2-4x+2