Fill in the missing powers of x in the dividend by having a coefficient of zero (0); then use long division:
_________________ 6x³ - 3x² - 2x + 1
________---------------------------------
2x + 1 | 12x⁴ + 0x³ - 7x² + 0x + 1
_________ 12x⁴ + 6x³
_________ -------------
_______________ - 6x³ - 7x²
_______________ - 6x³ - 3x²
_______________ -------------
____________________ - 4x² + 0x
____________________ - 4x² - 2x
____________________ ------------
____________________________ 2x + 1
____________________________ 2x + 1
____________________________ --------
__________________________________0
____________________________ =====
→ (12x⁴ - 7x² + 1) ÷ (2x + 1) = 6x³ - 3x² - 2x + 1 with no remainder.
6x3+29x2-40x-42 divided by 6x+5 Quotient: x2+4x-10 Remainder: 8
The dividend. Divident / Divisor = Quotient (plus remainder)
x3+3x2+6x+1 divided by x+1 Quotient: x2+2x+4 Remaider: -3
4x2 + 6x - 3 (with no remainder)
Quotient: 2x3-x2-14x+42 Remainder: -131 over (x+3)
6x3+29x2-40x-42 divided by 6x+5 Quotient: x2+4x-10 Remainder: 8
The dividend. Divident / Divisor = Quotient (plus remainder)
The quotient works out as: x^2+2x+4 and there is a remainder of -3
x3+3x2+6x+1 divided by x+1 Quotient: x2+2x+4 Remaider: -3
4x2 + 6x - 3 (with no remainder)
Quotient: 2x3-x2-14x+42 Remainder: -131 over (x+3)
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
4.8571
Dividend: 4x^4 -x^2 +17x^2 +11x +4 Divisor: 4x +3 Quotient: x^3 -x^2 +5x -1 Remainder: 7
To find the number, multiply the divisor and quotient, then add the remainder. 9 (divisor) times 6 is 54. 54 plus 7 is 61. The number is 61.
7.3333
Dividend: 6x^3 +29^2 -40x -42 Divisor: 6x +5 Quotient: x^2 +4x -10 Remainder: 8