If x^3 + 2x^2 - x - 2 = 0, then x =?

Question

possible answers...

+2, +1

+2, -1

+1, +2

+1, -2

Answer 1

First: factor - when you have 4 terms, group "like" terms....

(x^3 - x) + (2x^2 - 2) = 0

Sec: find a common factor for both sets of parenthesis...

x(x^2 - 1) + 2(x^2 - 1) = 0
(x^2 - 1)(x + 2) = 0

*Factor the 1st set of parenthesis....

(x+1)(x-1)(x+2) = 0

Third: solve the three x-variables; set them to equal "0"...

a. x + 1 = 0
First: subtract "1" from both sides...

x + 1 - 1 = 0 - 1
x = -1

b. x - 1 = 0
*Add "1" to both sides...

x - 1 + 1 = 0 + 1
x = 1

c. x + 2 = 0
*Subtract "2" from both sides...

x + 2 - 2 = 0 - 2
x = -2

Solutions: -1, -2, and 1

Answer 2

x^3 + 2x^2 - x - 2
= x^2(x+2) - 1(x +2) =(x^2 -1)(x+2)
= (x - 1) (x + 1) (x +2).
Then the equation x^3 + 2x^2 - x - 2 = 0 becomes:
(x - 1) (x + 1) (x +2) = 0.
So the roots are x = 1, - 1, -2. Answer.
None of the answers is complete.

Answer 3

The math shown by the first two answers you received is correct. X has three values and solving for X does give -1, 1 and -2.

However, if your choices are only one of the four, then the obvious correct answer is the fourth one. Because while X can be 1 or -1, it can ONLY be -2. All of the other answers have a +2, which would not work for the equation. So if those are your answers, then the fourth one is the only possible correct answer.

Answer 4

x^3 + 2x^2 - x - 2 = 0
sub in values to find answers:
let the equation be f(x)
f(x) = 0
f(a number)= after subbing everything in, u should get 0 as ans.
so that number will be f(1) after some guessing.
so,
f(1) = 0
therefore, (x-1) is a factor of the equation.
(x-1)(something) = 0

::work out the something by using long division::

then factorise the (something)and then you will get the factors which are the answers.

Answer 5

x^3 + 2x^2 - x - 2 = 0

We're in luck. We can solve this using a method called grouping. How grouping works is that we factor the first two terms and the last two terms. In this case, notice how the biggest factor out of the first two terms is x^2, and the second two terms is -1. That's how we factor.

x^2 (x + 2) - 1(x + 2) = 0

Now, we treat this as one big expression, and factor out (x + 2) out of both of these.

(x + 2) (x^2 - 1) = 0

Notice that the second set of brackets factors as a difference of squares. That give sus

(x + 2) (x - 1) (x + 1) = 0

And that means our solutions are

x = {-2, 1, -1}

It doesn't seem to fit *any* of the answers.