How do I factor out x^3+2x^2 -x-2?
回答 (12)
2008-11-23 7:01 am
✔ 最佳答案
x(x^2 - 1)+ 2(x^2 - 1) =(x^2 - 1)(x + 2) =
(x - 1)(x + 1)(x + 2)
2008-11-23 3:00 pm
Try splitting it up into two parts:
part 1:
x^3 + 2x^2, which equals x^2(x + 2)
part 2:
-x-2, which equals -(x+2)
Then you can take the (x+2) out of the whole thing to get
(x+2)*(x^2 - 1)
then you can factor x^2 - 1 using the standard formula
(x+2)*(x+1)*(x-1)
hope that helps!
part 1:
x^3 + 2x^2, which equals x^2(x + 2)
part 2:
-x-2, which equals -(x+2)
Then you can take the (x+2) out of the whole thing to get
(x+2)*(x^2 - 1)
then you can factor x^2 - 1 using the standard formula
(x+2)*(x+1)*(x-1)
hope that helps!
2008-11-23 3:03 pm
Try whole factors of 2, first.
(x - 1) is a factor because
1^3 + 2*1^2 - 1 - 2 = 1 + 2 - 1 - 2 = 0
x^3 + 2x^2 - x - 2 = x^3 - x^2 + 3x^2 - 3x + 2x - 2 =
= (x - 1)x^2 + 3x(x - 1) + 2(x - 1) = (x - 1)(x^2 + 3x + 2) =
= (x - 1)(x^2 + 2x*1.5 + 1.5^2 - 1.5^2 + 2) =
= (x - 1)[(x + 1.5)^2 - 2.25 + 2] = (x - 1)[(x + 1.5)^2 - 0.25] =
= (x - 1)[(x + 1.5)^2 - 0.5^2] = (x - 1)(x + 1.5 + 0.5)(x + 1.5 - 0.5) =
= (x - 1)(x + 2)(x + 1)
(x - 1) is a factor because
1^3 + 2*1^2 - 1 - 2 = 1 + 2 - 1 - 2 = 0
x^3 + 2x^2 - x - 2 = x^3 - x^2 + 3x^2 - 3x + 2x - 2 =
= (x - 1)x^2 + 3x(x - 1) + 2(x - 1) = (x - 1)(x^2 + 3x + 2) =
= (x - 1)(x^2 + 2x*1.5 + 1.5^2 - 1.5^2 + 2) =
= (x - 1)[(x + 1.5)^2 - 2.25 + 2] = (x - 1)[(x + 1.5)^2 - 0.25] =
= (x - 1)[(x + 1.5)^2 - 0.5^2] = (x - 1)(x + 1.5 + 0.5)(x + 1.5 - 0.5) =
= (x - 1)(x + 2)(x + 1)
2008-11-23 2:57 pm
factor out largest factor of x first
x^2(x + 2) - x -2
notice that -1 multiplied by -x-2 would change this to x+2
x^2(x + 2) -1 (x + 2)
notice that the x + 2 shows up in both parentheses
we can combine to create:
(x^2 - 1)(x + 2)
you can still factor x^2 -1 more, and there's your answer!:
(x+1)(x-1)(x+2)
x^2(x + 2) - x -2
notice that -1 multiplied by -x-2 would change this to x+2
x^2(x + 2) -1 (x + 2)
notice that the x + 2 shows up in both parentheses
we can combine to create:
(x^2 - 1)(x + 2)
you can still factor x^2 -1 more, and there's your answer!:
(x+1)(x-1)(x+2)
2008-11-23 4:25 pm
x^3 + 2x^2 - x - 2
= (x^3 + 2x^2) - (x + 2)
= x^2(x + 2) - 1(x + 2)
= (x + 2)(x^2 - 1)
= (x + 2)(x + 1)(x - 1)
= (x^3 + 2x^2) - (x + 2)
= x^2(x + 2) - 1(x + 2)
= (x + 2)(x^2 - 1)
= (x + 2)(x + 1)(x - 1)
2008-11-23 3:54 pm
x³ + 2x² - x - 2
x²(x + 2) - 1(x + 2)
(x² - 1)(x + 2)
(x - 1)(x + 1)(x + 2)
x²(x + 2) - 1(x + 2)
(x² - 1)(x + 2)
(x - 1)(x + 1)(x + 2)
2008-11-23 3:06 pm
x^2(x+2)-(x+2)=(x+2)(x^2-1)=
=(x+1)(x-1)(x-2)
=(x+1)(x-1)(x-2)
2008-11-23 3:04 pm
( x^2 -1 ) ( x +2 )
2008-11-23 3:01 pm
first take x^3+2x^2 -x-2 and right it as (x^3+2x^2) -x-2
Then factor out an x^2 to get x^2(x+2)-x-2.
Now factor out a negative sign from -x-2.
x^2(x+2)-(x+2). Now factor out x+2.
(x+2)(x^2-1). Now (x^2-1) is a difference of squares. So its (x-1)(x+1).
So now we have (x+2)(x-1)(x+1)=x^3+2x^2 -x-2
Then factor out an x^2 to get x^2(x+2)-x-2.
Now factor out a negative sign from -x-2.
x^2(x+2)-(x+2). Now factor out x+2.
(x+2)(x^2-1). Now (x^2-1) is a difference of squares. So its (x-1)(x+1).
So now we have (x+2)(x-1)(x+1)=x^3+2x^2 -x-2
2008-11-23 2:59 pm
First, group them: (x^3+2x^2)-(x+2)
then, pull out x^2: x^2(x+2)-(x+2)
then group them with x^2-1 and (x+2)
answer: (x^2-1)(x+2)
then, pull out x^2: x^2(x+2)-(x+2)
then group them with x^2-1 and (x+2)
answer: (x^2-1)(x+2)
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