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x3 + 2x2 - 35x = x(x2 + 2x - 35) = x(x + 7)(x - 5)
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.
I hope you mean x3+2x2-9x+18. Treat the equation like two equations: x3+2x2 and 9x+18. Factor out x2 from the first equation, so x2(x+2). Factor out 9 from the second equation, so 9(x+2). Now, the whole equation. x2(x+2)-9(x+2). Factor out (x+2), so (x+2)(x2-9). (x2-9) factors into (x+3)(x-3). So, (x+2)(x+3)(x-3) is the complete factorization. Hope this helps.
Choose the lowest of the exponents. The GCF of x3 and x5 is x3
x2(x - 8)