Question

divide 3x^4+4x^3+3x+1 by (x+1) and verify the relation P(x) = g(x) × q(x) + r(x)​

Answer 1

Answer:

$\mathrm{Long\:division\:\frac{3x^4+4x^3+3x+1}{\left(x+1\right)}:\quad 3x^3+x^2-x+4-\frac{3}{x+1}}$

Step-by-step explanation:

$\mathrm{\frac{3x^4+4x^3+3x+1}{\left(x+1\right)}}$

$=3x^3+\frac{x^3+3x+1}{x+1}$

$=3x^3+x^2+\frac{-x^2+3x+1}{x+1}$

$=3x^3+x^2-x+\frac{4x+1}{x+1}$

$=3x^3+x^2-x+4+\frac{-3}{x+1}$

$=3x^3+x^2-x+4-\frac{3}{x+1}$

Answer 2

Answer:

_________________

x+1 ) 3x^4 + 4x^3 + 3x + 1 ( 3x^3 + x^2 + x + 2

+ 3x^4 + 3x^3

- -

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

+ x^3 + 3x + 1

+ x^3 + x^2 +

-

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

+ x^2 + 3x + 1

+ x^2 + 1x

- -

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

+ 2x + 1

+ 2x + 2

- -

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

- 1

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

p(x) = g(x) × q(x) + r(x)

[ 3x^4 + 4x^3 + 3x 1 ] = [ x+1 ] × [ 3x^4 + 4x^3 + 3x + 1 ] + [ - 1 ]

= [ 3x^4 + 4x^3 + 3x + 2 ] + [ - 1 ]

= 3x^4 + 4x^3 + 3x + 1