Dividend: 4x^4 -x^2 +17x^2 +11x +4
Divisor: 4x +3
Quotient: x^3 -x^2 +5x -1
Remainder: 7
Quotient = x3 - x2 + 5x - 1Remainder = 7.
It is x^3 - x^2 + 5x - 1Further Information:-Dividend: 4x^4 -x^3 +17^2 +11x +4Divisor: 4x +3Quotient: x^3 -x^2 +5x -1Remainder: 7
Dividend: x3+4x2-9x-36 Divisor: x+3 Quotient: x2+x-12
That one, there!
-3
P(x) is a polynomial of order 4 and you are dividing by a polynomial of order 1 so the quotient will be of order 4 - 1 = 3 So suppose the quotient is Ax3 + Bx2 + Cx + D Then p(x)/(x + 2) = Ax3 + Bx2 + Cx + D with remainder R. To find R, simply evaluate p(x) at x = -2. p(2) = -24 Cross-multiply: p(x) = (x + 2)*(Ax3 + Bx2 + Cx + D) - 24 = Ax4 + 2Ax3 + Bx3 + 2Bx2 + Cx2 + 2Cx + Dx + 2D - 24 Comparing coefficients of: x4: 1 = A x3: 2 = 2A +B = 2 + B => B = 0 x2: 1 = 2B + C = 0 + C => C = 1 x : 8 = 2C + D = 2 + D => D = 6 and, as a check, x0 : -12 = 2D + R = 12 + R => R = -24
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
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)
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.
Dividend: 6x^3 +29^2 -40x -42 Divisor: 6x +5 Quotient: x^2 +4x -10 Remainder: 8
2x2-4x+5 divided by x-1 Quotient: 2x-2 Remainder: 3
Dividend: 4x^4 -x^3 +17x^2 +11x +4 Divisor: 4x +3 Quotient: x^3 -x^2 +5x -1 Remainder: 7
It is x^3 - x^2 + 5x - 1Further Information:-Dividend: 4x^4 -x^3 +17^2 +11x +4Divisor: 4x +3Quotient: x^3 -x^2 +5x -1Remainder: 7