x3 + 2x2 + 3x + 6 = x2(x + 2) + 3(x + 2) = (x + 2)(x2 + 3)
(x + 2)(x^2+4)
x3 + 8 = x3 + 23 = (x + 2)(x2 + 2x + 22) = (x + 2)(x2 + 2x + 4)
That depends on what the problem is. The expresion alone is not a problem. It's just an expression. Presumably, what you want to do here is to simplify it. We're given: (x - 2) / (x3 - 2x2 + x - 3) Let's start by tring to divide the numerator into the denominator using long division: x2 + 1 (x - 2) x3 - 2x2 + x - 3 x3 - 2x2 0 + x - 3 x - 2 -1 R Since we get a non-zero remainder, we can see that x - 2 is not a factor of the denominator. And in fact, looking further into it, we will find that the denominator can not be factored, and so this problem can not be simplified.
(x-2)(x^2+3)
x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)
x3 - 2x2 - 4x + 8 = (x2 - 4)(x - 2) = (x + 2)(x - 2)(x - 2)
x3 + 2x2 + 3x + 6 = x2(x + 2) + 3(x + 2) = (x + 2)(x2 + 3)
(x + 2)(x^2+4)
If that's 2x2, the answer is (x + 2)(x2 + 4)
x3 + 8 = x3 + 23 = (x + 2)(x2 + 2x + 22) = (x + 2)(x2 + 2x + 4)
(x - y)(x^2 + xy + y^2
x^2(x + 2) - 1(x+2) (x+2)(x-1)(x+1)
The factor theorem states that for any polynomial function f(x), if f(a) = 0, then (x-a) is a factor of f(x). Let f(x) = x3-2x2-8x-5. If (x+1) is a factor, then f(-1) = 0. (x+1 = x - (-1)) Input x = -1 into f: (-1)3-2(-1)2-8(-1)-5 f(-1) = -1 -2 + 8 - 5 f(-1) = 0. Since f(-1) = 0, (x+1) is a factor of x3-2x2-8x-5. Q.E.D.
That depends on what the problem is. The expresion alone is not a problem. It's just an expression. Presumably, what you want to do here is to simplify it. We're given: (x - 2) / (x3 - 2x2 + x - 3) Let's start by tring to divide the numerator into the denominator using long division: x2 + 1 (x - 2) x3 - 2x2 + x - 3 x3 - 2x2 0 + x - 3 x - 2 -1 R Since we get a non-zero remainder, we can see that x - 2 is not a factor of the denominator. And in fact, looking further into it, we will find that the denominator can not be factored, and so this problem can not be simplified.
x3 + 6x2 - 4x - 24 = (x + 6)(x2 - 4) = (x + 6)(x + 2)(x - 2)
(x-2)(x^2+3)