(x3 + 3x2 - 2x + 7)/(x + 1) = x2 + 2x - 4 + 11/(x + 1)
(multiply x + 1 by x2, and subtract the product from the dividend)
1. x2(x + 1) = x3 + x2
2. (x3 + 3x2 - 2x + 7) - (x3 + x2) = x3 + 3x2 - 2x + 7 - x3 - x2 = 2x2 - 2x + 7
(multiply x + 1 by 2x, and subtract the product from 2x2 - 2x + 7)
1. 2x(x + 1) = 2x2 + 2x
2. (2x2 - 2x + 7) - (2x2 + 2x) = 2x2 - 2x + 7 - 2x2 - 2x = -4x + 7
(multiply x + 1 by -4, and subtract the product from -4x + 7)
1. -4(x + 1) = -4x - 4
2. -4x + 7 - (-4x - 4) = -4x + 7 + 4x + 4 = 11(remainder)
== == Suppose f(x) = x3 + 3x2 - 2x + 7 divisor is x + 1 = x - (-1); so rem = f(-1) = 11
x3+3x2+6x+1 divided by x+1 Quotient: x2+2x+4 Remaider: -3
(x4 + y4)/(x + y) = Quotient = x3 - x2y + xy2 - y3 Remainder = - 2y4/(x+y) So, x3 - x2y + xy2 - y3 - 2y4/(x+y)
The answer to x4+x3-14x2+4x+6 divided by x-3 is x3+4x2-2x-2
x3-x2+5x-1 with remainder 7, which the final answer would be written as:x3-x2+5x-1+[7/(4x+3)]
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
That depends on whether or not 2x is a plus or a minus
== == Suppose f(x) = x3 + 3x2 - 2x + 7 divisor is x + 1 = x - (-1); so rem = f(-1) = 11
x3+3x2+6x+1 divided by x+1 Quotient: x2+2x+4 Remaider: -3
Dividend: 4x^4 -x^2 +17x^2 +11x +4 Divisor: 4x +3 Quotient: x^3 -x^2 +5x -1 Remainder: 7
(x4 + y4)/(x + y) = Quotient = x3 - x2y + xy2 - y3 Remainder = - 2y4/(x+y) So, x3 - x2y + xy2 - y3 - 2y4/(x+y)
The answer to x4+x3-14x2+4x+6 divided by x-3 is x3+4x2-2x-2
4
(-x3 + 75x - 250) / (x + 10) = x2 - 10x - 25
The inverse of a number is 1 divided by that number. So the inverse of x3 + 1 is 1/(x3 + 1).
2x2+7/x1
True.