Sure, let's factor each polynomial completely step by step.
### Polynomial 1:
[tex]\[ 2x^8 + 4x^2 \][/tex]
1. Identify the common factors:
Both terms [tex]\(2x^8\)[/tex] and [tex]\(4x^2\)[/tex] have a common factor of [tex]\(2x^2\)[/tex].
2. Factor out the greatest common factor (GCF):
Factoring out [tex]\(2x^2\)[/tex] from each term, we get:
[tex]\[ 2x^8 + 4x^2 = 2x^2(x^6 + 2) \][/tex]
Thus, the factored form of [tex]\( 2x^8 + 4x^2 \)[/tex] is:
[tex]\[ 2x^2(x^6 + 2) \][/tex]
### Polynomial 2:
[tex]\[ 6x + 10x^2 \][/tex]
1. Identify the common factors:
Both terms [tex]\(6x\)[/tex] and [tex]\(10x^2\)[/tex] have a common factor of [tex]\(2x\)[/tex].
2. Factor out the GCF:
Factoring out [tex]\(2x\)[/tex] from each term, we get:
[tex]\[ 6x + 10x^2 = 2x(3 + 5x) \][/tex]
Thus, the factored form of [tex]\( 6x + 10x^2 \)[/tex] is:
[tex]\[ 2x(3 + 5x) \][/tex]
### Polynomial 3:
[tex]\[ 14x^3 - 2x^3 \][/tex]
1. Combine the like terms:
[tex]\[ 14x^3 - 2x^3 = (14 - 2)x^3 = 12x^3 \][/tex]
2. Factor out the GCF (Since we simplified it already, this step doesn't change the polynomial):
[tex]\[ 12x^3 = 2x^3(6) \][/tex]
Thus, the factored form of [tex]\( 12x^3 \)[/tex] is:
[tex]\[ 2x^3(6) \][/tex]
So, the final factored forms of the given polynomials are:
1. [tex]\[ 2x^2(x^6 + 2) \][/tex]
2. [tex]\[ 2x(3 + 5x) \][/tex]
3. [tex]\[ 2x^3(6) \][/tex]
