Question

Divide (4x⁴ + 9x³ +4x² +5x +2) by (x+2)​

Answer 1

Solution:

By direct method

x+2)4x⁴+9x³+4x²+5x+2)4x³+x²+2x+1

⠀⠀⠀4x⁴+8x³

⠀⠀⠀(-)⠀(-)

⠀⠀__________

⠀⠀⠀⠀⠀⠀x³+4x²

⠀⠀⠀⠀⠀⠀x³+2x²

⠀⠀⠀⠀⠀(-)⠀(-)

⠀⠀______________

⠀⠀⠀⠀⠀⠀⠀⠀2x²+5x

⠀⠀⠀⠀⠀⠀⠀⠀2x²+4x

⠀⠀⠀⠀⠀⠀⠀(-)⠀⠀(-)

⠀⠀________________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x+2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x+2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(-)⠀(-)⠀

⠀⠀__________________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀0

Quotient=4x³+x²+2x+1

Remainder=0

_______________________________

Verification:

Divided=Quotient×Divisor+Remainder

L.H.S.=4x⁴+9x³+4x²+5x+2

R.H.S.=(4x³+x²+2x+1)(x+2)+0

⠀⠀⠀⠀=4x⁴+x³+2x²+x+8x³+2x²+4x+2

⠀⠀⠀⠀=4x⁴+x³+8x³+2x²+2x²+x+4x+2

⠀⠀⠀⠀=4x⁴+9x³+4x²+5x+2

⠀⠀⠀⠀=L.H.S.

Hence, verified.

Answer 2

Answer:

4x³+x²+2x+1

Step-by-step explanation:

x+2)4x⁴ + 9x³ +4x² +5x +2( 4x³+x²+2x+1

4x⁴+8x³

- -

x³+4x²

x³+2x²

- -

2x²+5x

2x²+4x

- -

x+2

x+2

- -

0