Answer :
Sure! Let's factor the greatest common factor (GCF) out of the polynomial [tex]\(35x^5 + 15x^3 + 5x^2\)[/tex] step by step.
### Step-by-Step Solution:
1. Identify the GCF of the coefficients:
- The coefficients of the polynomial are 35, 15, and 5.
- The greatest common factor of these numbers is 5.
2. Identify the smallest power of [tex]\(x\)[/tex] in the terms:
- The polynomial terms are [tex]\(35x^5\)[/tex], [tex]\(15x^3\)[/tex], and [tex]\(5x^2\)[/tex].
- The smallest power of [tex]\(x\)[/tex] is [tex]\(x^2\)[/tex].
3. Factor the GCF out of each term:
- Factor out [tex]\(5x^2\)[/tex] from each term.
- [tex]\(35x^5 \div 5x^2 = 7x^3\)[/tex]
- [tex]\(15x^3 \div 5x^2 = 3x\)[/tex]
- [tex]\(5x^2 \div 5x^2 = 1\)[/tex]
4. Write the factored form:
- The factored form of the polynomial is [tex]\(5x^2(7x^3 + 3x + 1)\)[/tex].
So, the factored form of the polynomial [tex]\(35x^5 + 15x^3 + 5x^2\)[/tex] by factoring out the GCF is:
[tex]\[ 5x^2(7x^3 + 3x + 1) \][/tex]
That's the solution!
### Step-by-Step Solution:
1. Identify the GCF of the coefficients:
- The coefficients of the polynomial are 35, 15, and 5.
- The greatest common factor of these numbers is 5.
2. Identify the smallest power of [tex]\(x\)[/tex] in the terms:
- The polynomial terms are [tex]\(35x^5\)[/tex], [tex]\(15x^3\)[/tex], and [tex]\(5x^2\)[/tex].
- The smallest power of [tex]\(x\)[/tex] is [tex]\(x^2\)[/tex].
3. Factor the GCF out of each term:
- Factor out [tex]\(5x^2\)[/tex] from each term.
- [tex]\(35x^5 \div 5x^2 = 7x^3\)[/tex]
- [tex]\(15x^3 \div 5x^2 = 3x\)[/tex]
- [tex]\(5x^2 \div 5x^2 = 1\)[/tex]
4. Write the factored form:
- The factored form of the polynomial is [tex]\(5x^2(7x^3 + 3x + 1)\)[/tex].
So, the factored form of the polynomial [tex]\(35x^5 + 15x^3 + 5x^2\)[/tex] by factoring out the GCF is:
[tex]\[ 5x^2(7x^3 + 3x + 1) \][/tex]
That's the solution!
