Factor completely:
1. 8x3 + 2x3 – 12x –3
2. 27x3+8
3.125 – 8x3
To factor completely, we need to find the common factors in each expression and then factor them out.
1. 8x^3 + 2x^3 - 12x - 3
First, let's look for the common factors in each term. The terms 8x^3 and 2x^3 have the common factor of x^3. The terms -12x and -3 do not share any common factor other than 1.
So, we can factor out the common factor of x^3:
x^3(8 + 2) - 3(4x + 1)
Simplifying further:
x^3(10) - 3(4x + 1)
Finally, we have the completely factored form:
10x^3 - 12x - 3
2. 27x^3 + 8
In this expression, there are no common factors in each term other than 1. So, the expression is already in its factored form.
3. 125 - 8x^3
Again, there are no common factors in each term other than 1. However, we can recognize that 125 and 8 are perfect cubes. 125 is the cube of 5 (5^3) and 8 is the cube of 2 (2^3).
Using the formula (a^3 - b^3) = (a - b)(a^2 + ab + b^2), we can factor the expression:
125 - 8x^3 = (5 - 2x)(25 + 10x + 4x^2)
So, the completely factored form is:
(5 - 2x)(25 + 10x + 4x^2)