x3 + 2x2 - 8x + 5 = 0 x(2x - 8) + 5 = 0
Factor out an X X(X^2 - 12X + 35) factor quadratic equation X(X - 7)(X - 5) ------------------- fully factored
x3 + 2x2 + 3x + 6 = x2(x + 2) + 3(x + 2) = (x + 2)(x2 + 3)
(x + 2)(x^2+4)
(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 + x22. (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 + 2x2. (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 - 42. -4x + 7 - (-4x - 4) = -4x + 7 + 4x + 4 = 11(remainder)
it is below 555 and above 200 * * * * * x3 - 2x2 + 35x = x*(x2 - 2x - 35) = x*(x + 5)*(x - 7)
x(x + 5)(x - 7)
x3 - 12x2 + 35x = x (x2 - 12x + 35) = x (x - 7) (x - 5)
x3 + 2x2 - 35x = x(x2 + 2x - 35) = x(x + 7)(x - 5)
x3 - 12x2 + 35x = x(x2 - 12x + 35) = x(x - 5)(x - 7)
x^(3) - 12x^(2) + 35 x Factor out 'x' Hence x(x^(2) - 12x + 35) Factor the quadratic x(x - 5)(x - 7) Done!!!!!
x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)
x3 + 2x2 - 8x + 5 = 0 x(2x - 8) + 5 = 0
Factor out an X X(X^2 - 12X + 35) factor quadratic equation X(X - 7)(X - 5) ------------------- fully factored
x3 + 2x2 + 3x + 6 = x2(x + 2) + 3(x + 2) = (x + 2)(x2 + 3)
x3 - 2x2 - 4x + 8 = (x2 - 4)(x - 2) = (x + 2)(x - 2)(x - 2)
2x2+7/x1