Question

Consider the binomial 4x3 – 32. Is there a GCF > 1 for the two terms? The completely factored form of this polynomial is (x2 + 2x + 4).

Answer 1

Answer:

....Yes it is 4                                                                                                                       ....4(x-2)

Step-by-step explanation:

the screenshot shows proof :))

Answer 2

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)