Factor completely -5x3 + 10^2
-5x3 + 10^2
First, we can factor out a common factor of -5:
-5(x3 - 2^2)
We can then notice that x3 - 2^2 is the difference of two squares, since 2^2 = 4:
-5((x)^2 - 2^2)
We can use the formula for the difference of squares to factor further:
-5(x + 2)(x - 2)^2
Therefore, the expression factors completely as -5(x + 2)(x - 2)^2.
To factor completely, we need to first write the expression in factored form.
The given expression is -5x^3 + 10^2.
Let's factor out the greatest common factor (GCF) from both terms. The GCF of -5x^3 and 100 is 5.
So, we can rewrite the expression as 5(-x^3 + 20).
Now, let's factor out the negative sign and rewrite the expression as -5(x^3 - 20).
We can further factor this expression, but it cannot be factored completely because x^3 - 20 is not a perfect cube and 20 is not a perfect cube either.
Therefore, the factored form of -5x^3 + 10^2 is -5(x^3 - 20).