Answer :
To factor the greatest common factor (GCF) out of the polynomial [tex]\(35x^5 + 10x^3 + 5x^2\)[/tex], follow these steps:
1. Identify the Coefficients:
The coefficients of the terms in the polynomial are 35, 10, and 5.
2. Find the GCF of the Coefficients:
Determine the GCF of the coefficients 35, 10, and 5. The greatest common factor of these numbers is 5.
3. Factor out the GCF:
Divide each term in the polynomial by the GCF (which is 5), and rewrite the polynomial:
- Divide [tex]\(35x^5\)[/tex] by 5: [tex]\((35 \div 5)x^5 = 7x^5\)[/tex]
- Divide [tex]\(10x^3\)[/tex] by 5: [tex]\((10 \div 5)x^3 = 2x^3\)[/tex]
- Divide [tex]\(5x^2\)[/tex] by 5: [tex]\((5 \div 5)x^2 = 1x^2\)[/tex]
4. Write the Factored Expression:
The factored form of the polynomial is obtained by taking out the GCF (5) and writing the remaining polynomial:
[tex]\[
35x^5 + 10x^3 + 5x^2 = 5(7x^5 + 2x^3 + x^2)
\][/tex]
This is the polynomial with the GCF factored out. The expression inside the parentheses, [tex]\(7x^5 + 2x^3 + x^2\)[/tex], is the result of dividing each term by the GCF of 5.
1. Identify the Coefficients:
The coefficients of the terms in the polynomial are 35, 10, and 5.
2. Find the GCF of the Coefficients:
Determine the GCF of the coefficients 35, 10, and 5. The greatest common factor of these numbers is 5.
3. Factor out the GCF:
Divide each term in the polynomial by the GCF (which is 5), and rewrite the polynomial:
- Divide [tex]\(35x^5\)[/tex] by 5: [tex]\((35 \div 5)x^5 = 7x^5\)[/tex]
- Divide [tex]\(10x^3\)[/tex] by 5: [tex]\((10 \div 5)x^3 = 2x^3\)[/tex]
- Divide [tex]\(5x^2\)[/tex] by 5: [tex]\((5 \div 5)x^2 = 1x^2\)[/tex]
4. Write the Factored Expression:
The factored form of the polynomial is obtained by taking out the GCF (5) and writing the remaining polynomial:
[tex]\[
35x^5 + 10x^3 + 5x^2 = 5(7x^5 + 2x^3 + x^2)
\][/tex]
This is the polynomial with the GCF factored out. The expression inside the parentheses, [tex]\(7x^5 + 2x^3 + x^2\)[/tex], is the result of dividing each term by the GCF of 5.
