(x + 4) / (x3 - 11x + 20)
= (x + 4) / (x2 + 4x - 5)(x + 4)
= 1 / (x2 + 4x - 5)
= 1 / (x + 5)(x - 1), where x ≠ -4
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Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
The inverse of a number is 1 divided by that number. So the inverse of x3 + 1 is 1/(x3 + 1).
That depends on whether or not 2x is a plus or a minus
x3 + 2x2 - 19x - 20 = x3 + x2 + x2 + x - 20x - 20 = x2(x + 1) - x(x + 1) - 20(x + 1) = (x + 1)(x2 + x - 20) = (x + 1)(x - 4)(x + 5)
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)