Sure! Let's factor each polynomial step-by-step.
### 1. Polynomial: [tex]\(2x^8 + 4x^2\)[/tex]
Step 1: Identify common factors in each term.
- Both terms have a common factor of [tex]\(2x^2\)[/tex].
Step 2: Factor out the common factor [tex]\(2x^2\)[/tex].
[tex]\[ 2x^8 + 4x^2 = 2x^2(x^6) + 2x^2(2) \][/tex]
Step 3: Combine the factored terms.
[tex]\[ 2x^8 + 4x^2 = 2x^2(x^6 + 2) \][/tex]
So, the factored form of [tex]\(2x^8 + 4x^2\)[/tex] is:
[tex]\[ 2x^2(x^6 + 2) \][/tex]
### 2. Polynomial: [tex]\(6x + 10x^2\)[/tex]
Step 1: Identify common factors in each term.
- Both terms have a common factor of [tex]\(2x\)[/tex].
Step 2: Factor out the common factor [tex]\(2x\)[/tex].
[tex]\[ 6x + 10x^2 = 2x(3) + 2x(5x) \][/tex]
Step 3: Combine the factored terms.
[tex]\[ 6x + 10x^2 = 2x(3 + 5x) \][/tex]
So, the factored form of [tex]\(6x + 10x^2\)[/tex] is:
[tex]\[ 2x(3 + 5x) \][/tex]
### 3. Polynomial: [tex]\(3 \cdot 14x^3 - 2x^3\)[/tex]
Step 1: Simplify the coefficients in the terms.
[tex]\[ 3 \cdot 14x^3 - 2x^3 = 42x^3 - 2x^3 \][/tex]
Step 2: Combine like terms.
[tex]\[ 42x^3 - 2x^3 = (42 - 2)x^3 = 40x^3 \][/tex]
So, the factored form of [tex]\(3 \cdot 14x^3 - 2x^3\)[/tex] is:
[tex]\[ 40x^3 \][/tex]
Hence, the completely factored forms are:
1. [tex]\(2x^8 + 4x^2 = 2x^2(x^6 + 2)\)[/tex]
2. [tex]\(6x + 10x^2 = 2x(3 + 5x)\)[/tex]
3. [tex]\(3 \cdot 14x^3 - 2x^3 = 40x^3\)[/tex]
