Question

Describe the steps you would use to factor 2x3 + 5x2 – 8x – 20 completely. Then state the factored form.

Answer 1

The polynomial $2x^3 + 5x^2-8x-20$ may have solutions which are the divisors of -20, therefore -20 has the following divisors: $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$.
If x=1, then $2\cdot1^3 + 5\cdot1^2-8\cdot1-20=-20\neq 0$,
if x=-1, then $2\cdot(-1)^3 + 5\cdot(-1)^2-8\cdot(-1)-20=-9\neq 0$,
if x=2, then $2\cdot2^3 + 5\cdot2^2-8\cdot2-20=0$, then x=2 is a solution and you have the first factor (x-2). 
If x=-2, then $2\cdot(-2)^3 + 5\cdot(-2)^2-8\cdot(-2)-20=0$, then x=-2 is a solution, so you have the second factor (x+2).
Since x-2 and x+2 are two factors of $2x^3 + 5x^2-8x-20$ , then the polynomial $x^2-4$ is a divisor of $2x^3 + 5x^2-8x-20$ and dividing the polynomial $2x^3 + 5x^2-8x-20$ by $x^2-4$ you obtain 
 $2x^3 + 5x^2-8x-20=(x-2)(x+2)(2x+5)$.

Answer 2

You have the polynomial 2x³+5x²-8x-20=0
 To factor you must apply the steps shown below:
 1. Form two groups and factor the Greatest Common Factor of both groups, which are x² and 4
 x²(2x+5)-4(2x+5)=0
 2. Combine both groups to obtain a monomial:
 (x²-4)(2x+5)=0
 3. Factor (x²-4) by Difference of squares:
 (x-2)(x+2)(2x+5)=0
 4. Then you obtain the following result:
 x=2
 x=-2
 x=-5/2 
 It can be factor by using the Greatest Common Factor and the Difference of squares.