how do i factor this?
2x^3+4x^2+2x
= 2x(x^2 + 2x + 1)
= 2x(x+1)(x+1) or 2x(x+1)^2
well the original equation was 4x^3+8x^2+4x
then i factored that to 2(2x^3+4x^2+2x)
so that where i got lost and your answer doesn't give me that, so confused!
well, you gave me the expression without the factor of 2 in front, so ...
multiply me answer by 2 and you will have it.
so ...
2( my answer)
= 4x(x+1)(x+1) or 4x(x+1)^2
expand my answer and you will get
4x^3+8x^2+4x
To factor the given expression 2x^3 + 4x^2 + 2x, we can follow these steps:
Step 1: Find the greatest common factor (GCF) of all the terms, if possible. In this case, all terms share a common factor of 2x:
2x^3 + 4x^2 + 2x
= 2x(x^2 + 2x + 1)
Step 2: Now, we need to check if the quadratic expression inside the parentheses (x^2 + 2x + 1) can be further factored. To do this, we can examine if it is a perfect square trinomial.
a. Check if the quadratic expression can be written in the form (ax + b)^2 where a and b are constants.
The given quadratic expression, x^2 + 2x + 1, cannot be written in the form (ax + b)^2 because the coefficient of the linear term (2x) is not twice the product of the square root of the first term (x).
b. Therefore, the quadratic expression cannot be factored further.
So, the factored form of the expression 2x^3 + 4x^2 + 2x is 2x(x^2 + 2x + 1).