That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: (7 plus or minus the square root of 145) divided by 16.
p = 1.1900996611745185
p = -0.3150996611745185
x2(x - 8)
(x+2)(x2+2x+4)
Choose the lowest of the exponents. The GCF of x3 and x5 is x3
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.
(x - 6)(x2 + 6x + 36)
y5(x3 - 8)
x2(x - 8)
x3 + 8 = x3 + 23 = (x + 2)[x2 - (x)(2) + 22] = (x + 2) (x2 - 2x + 4)
x3 + 8 = x3 + 23 = (x + 2)(x2 + 2x + 22) = (x + 2)(x2 + 2x + 4)
(x+2)(x2+2x+4)
(x - 8)(x2 + 8x + 64)
x3 - 2x2 - 4x + 8 = (x2 - 4)(x - 2) = (x + 2)(x - 2)(x - 2)
x3-343
(x - 2)(x^2 + 2x + 4)
x3 + 3x2 - 6x - 8 = (x - 2)(x2 + 5x + 4) = (x - 2)(x + 1)(x + 4)
Since x3 is a factor of x5, it is automatically the GCF.
Greatest common factor of x4 and x3 is x3.