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x3-x2+5x-1 with remainder 7, which the final answer would be written as:x3-x2+5x-1+[7/(4x+3)]
x2 + 5x + 25
x3 - 4x2 + 5x - 20 = x2*(x - 4) + 5*(x - 4) = (x2 + 5)*(x - 4)
Difference of two cubes: a3 - b3 = (a-b)(a2+ab+b2) 125 - x3 = 53 - x3 = (5 - x)(52 + 5x + x2) = (5 - x)(25 + 5x + x2)
(x - 1)(x^2 - 5)
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
Dividend: 4x^4 -x^2 +17x^2 +11x +4 Divisor: 4x +3 Quotient: x^3 -x^2 +5x -1 Remainder: 7
x3 + 2x2 + 5x + 4 = (x + 1)(x2 + x + 4)
x3-x2+5x-1 with remainder 7, which the final answer would be written as:x3-x2+5x-1+[7/(4x+3)]
1.6667
10x + 5 unless you know what x & y are * * * * * Perhaps this answer will be of help: x3 + x2 + 5x + 5 = (x + 1)(x2 + 5). If you are willing to go to complex roots, then, x3 + x2 + 5x + 5 = (x + 1)(x2 + 5). = (x + 1)(x + i√5)(x - i√5); in which case, x = -1 or ±i√5.
x2 + 5x + 25
x3 - 4x2 + 5x - 20 = x2*(x - 4) + 5*(x - 4) = (x2 + 5)*(x - 4)
x3 + 12x2 - 5x = x(x2 + 12x - 5) = x(x + 6 - √41)(x + 6 + √41)
Difference of two cubes: a3 - b3 = (a-b)(a2+ab+b2) 125 - x3 = 53 - x3 = (5 - x)(52 + 5x + x2) = (5 - x)(25 + 5x + x2)
x3 -3x2 -x - 1 divided by x+2 equals x2-5x+9 remainder -19 It's difficult to show how to work it out on this computer but division with algebra has a lot in common with doing long division with integers.
Remainder Theorem:- When f(x) is divided by (x-a) the remainder is f(a) Tor example:- f(x) x3-2x2+5x+8 divided by x-2 f(2) 8-8+10+8 = 18 So the remainder is 18 if there is no remainder then the divisor is a factor of the dividend.