Answer:
Yes there is GCF > 1 ⇒ (GCF = 4)
The completely factored form is 4(x - 2)(x² + 2x + 4)
Step-by-step explanation:
* Lets find the greatest common factor of the two terms
- The binomial is 4x³ - 32
- The terms of the binomial are 4x³ and 32
- The greatest common factor of 4 and 32 is 4 because both of them
can divided by 4
∵ 4x³ ÷ 4 = x³
∵ 32 ÷ 4 = 8
∴ The greatest common factor GCF is 4
∴ 4x³ - 32 = 4(x³ - 8)
* Yes there is GCF > 1
# x³ - 8 is the difference of two cubs, it can factorize it into two
brackets
- The first bracket has cube root of x³ and cube root of 8
- The second bracket comes from the first bracket it has three terms
# The 1st term is square the 1st term in the first bracket
# The 2nd term is the product of the 1st term and the 2nd term of the
1st bracket with opposite sign of the 2nd term in the 1st bracket
# The 3rd term is the square of the 2nd term in the 1st bracket
* Lets do these steps with x³ - 8
∵ The first bracket = (∛x³ - ∛8)
∵ ∛x³ = x and ∛8 = 2
∴ The first bracket = (∛x³ - ∛8) = (x - 2)
- Lets make the 2nd bracket from the 1st bracket
∴ The second bracket = (x² + (x)(2) + 2²)
∴ The second bracket = (x² + 2x + 4)
∴ The factorization of x³ - 8 = (x - 2)(x² + 2x + 4)
* The completely factored form is 4(x - 2)(x² + 2x + 4)
