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\\eq 0`,
if x=-1, then
`2\cdot(-1)^3 + 5\cdot(-1)^2-8\cdot(-1)-20=-9\\eq 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.