How do you factor 1/2x^3-x so that the zeroes can be found? Thank you-Adriana
I think you mean
1/(2x^3-x)
factoring the denominator
x(2x^2-1)= x(xsqrt2-1)(xsqrt2+1)
(1/2)x(x^2 - 2) = 0
x = 0 or x = ± √2
See how the same question can be interpreted in more than one way if you don't use brackets?
I read it as (1/2)x^3-x
bobpursley read it as 1/(2x^3-x)
or why not 1/(2x^3) - x ?
To factor the expression 1/2x^3 - x and find its zeros, we can follow these steps:
Step 1: Factor out the greatest common factor (GCF) if possible.
In this case, the GCF of the terms is x. Factoring out x gives us:
x(1/2x^2 - 1)
Step 2: Factor the remaining expression inside the parentheses.
Now, we need to factor the expression 1/2x^2 - 1. This is a difference of squares because 1/2x^2 is the square of (√1/2x) and 1 is the square of (√1). The difference of squares formula is a^2 - b^2 = (a + b)(a - b).
Here, a = √1/2x and b = √1.
So, applying the difference of squares formula, we have:
(√1/2x + √1)(√1/2x - √1)
Simplifying further, we have:
(√1/2x + 1)(√1/2x - 1)
Step 3: Combine the factors.
Finally, combine the factors to get the factored form of the expression:
x(√1/2x + 1)(√1/2x - 1)
Now, to find the zeros of the expression, set each factor equal to zero and solve for x:
x = 0 (from the factor x)
√1/2x + 1 = 0
√1/2x - 1 = 0
By solving these equations, you can find the values of x that make the expression equal to zero, which are the zeros of the expression.