x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)
x3 + 12x2 - 5x = x(x2 + 12x - 5) = x(x + 6 - √41)(x + 6 + √41)
x3 - 4x2 + x + 6 = (x + 1)(x - 2)(x - 3)
x3 - 2x2 - 4x + 8 = (x2 - 4)(x - 2) = (x + 2)(x - 2)(x - 2)
x3 - 10x2 + 24x = x(x2 - 10x + 24) = x(x2 - 4x - 6x + 24) = x[ x(x - 4) - 6(x - 4) ] = x(x - 6)(x - 4)
x3 + 6x2 - 4x - 24 = (x + 6)(x2 - 4) = (x + 6)(x + 2)(x - 2)
X3 - 4 = 2 X3 = 6 X = 61/3 X = about 1.817
x3 + 2x2 + 3x + 6 = x2(x + 2) + 3(x + 2) = (x + 2)(x2 + 3)
x3 + 2x2 - 5x - 6 = x3 + x2 + x2 + x - 6x - 6 = x2(x + 1) + x(x + 1) - 6(x + 1) = (x + 1)(x2 + x - 6) = (x + 1)(x2 + 3x - 2x - 6) = (x + 1)[x(x + 3) - 2(x + 3)] = (x + 1)(x + 3)(x - 2)
(x-2)(x^2+3)
The answer to x4+x3-14x2+4x+6 divided by x-3 is x3+4x2-2x-2
(x - 2)(x + 4)(x - 6)
x3 - 4x2 + x + 6 The sum of the odd coefficients equals the sum of the even coefficients, so (x + 1) is a factor. So x3 - 4x2 + x + 6 = x3 + x2 - 5x2 - 5x + 6x + 6 = x2(x + 1) - 5x(x + 1) + 6(x + 1) = (x + 1)(x2 - 5x + 6) = (x + 1)(x - 2)(x - 3)
-2
x3 + 8 = x3 + 23 = (x + 2)[x2 - (x)(2) + 22] = (x + 2) (x2 - 2x + 4)
9
(x + 2)(x^2 + 2x + 3)