factor x^3+2x^2?

Question

i know that the answer is x^2(x+2) -- i have a calculator -- but i want to know how one would come to that answer.

Answer 1

Starting with:
x³ + 2x²

As others have said, you just need to factor out the common x² (using the distributive property).

If it helps, you can think of this as:
x * x * x + 2 * x * x

Just group the common x * x as follows:
( x * x ) * x + ( x * x ) * 2

Now use the distributive property -- e.g. a * b + a * c = a * (b + c)
( x * x ) ( x + 2 )

So that's it, just turn x * x back into x²
x² ( x + 2 )

And a way to check this would be to just go in reverse... distribute the x² through and you'll see it is equivalent to your original equation of x³ + 2x²

Answer 2

In order to factor you have to "pull out" or remove numbers that are common to both terms--in your case--x^3 and x^2 and put them on the other side of the parenthesis.

So, x^2 is the most you can "pull out" because that's what's in 2x^2.

So, once that is removed, you get

x^2(x+2).

To check the answer, x^2 times x will become x^3 and x^2 x 2 is 2x^2.

Nice work and good luck.

Mysstere

Answer 3

well you see in multiplication,
x^n * x^k = x^(n+k)
similarly, x^2 * x = x^3

so in the expression x^3 + 2x^2, take x^2 out as it's common to both terms- then,
x^2 (x + 2)
Note that if you multiply out the brackets as given for a general case above you get the original expression.

Hope this helps! You oughta avoid using a calculator for algebra unless you need to find factors of equations in the third or higher degrees.

Answer 4

On the two sides of the '+' sign, you have a common "x^2". Therefore, you can factor it out and write out the remainder:

x^2(x+2)...using the distributive property, you can check your work by multiplying back to get your original x^3+2x^2.

Answer 5

Factoring is basically like making the numbers as small as possble. If you wanted to factor x^3+2x^2 you can take an x^2 out. divide the entire equation by x^2

Answer 6

When factoring, you try and pull out what is the common between the equative factors you have, in this case x^3 and 2x^2.
So by evaluation and the distributive property
a(b+c) = ab+ac, we can see x^2 is common between the elements. Working backwards you get
x^2(x+2), which is your answer.
Hope that helps !!

Answer 7

Ok. What you do first is look to see what the terms both have in common. In this case they bot have an x, and the lowest power is 2, so you can factor out an x^2. That's how you get x^2 (x+2).

Answer 8

(x+2)(x^2) the answer is got when you multiply the first factor by the second we get the original equation. Guess the first one and write the second from first. Guessing is done as follows. Make the first element of first factor as x try seeing what makes the second factor from this.

Answer 9

Use synthetic division. or take x^2 common term.