need help for math homework

Question

Find the quotient and remainder when  is divided by .

Answer 1

| 9x³ - 35x² + 140 x - 572

x +4 | 9x⁴ + x³ + 0x² -12x + 21

9x⁴+36x³

0 - 35x³ + 0x²

-35x³ - 140x²

0 + 140x² -12x

140x² + 560x

0 - 572x + 21

-572x - 2288

0 - 2309 ( remain)

Answer: 9x³ - 35x² + 140x - 572 remain -2309

Answer 2

x+4 is a factor means x=-4 is a solution

-4 | 9 1 0 -12 21

-36 140 -560 2288

_______________________________

9 -35 140 -572 2309

the quotient is 9x^3-35x^2 + 140x - 572 with remainder 2309

checki: (9x^3-35x^2+140x-572)(x+4) + 2309 =

9x^4 - 35x^3 + 140x^2 - 572x

36x^3 -140x^2 + 560x - 2288 + 2309

9x^4 + x - 12x + 21 which is the same dividend