IDNLearn.com provides a comprehensive platform for finding accurate answers. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.
Sagot :
Sure! Let's factor the polynomial [tex]\( 35s^6 + 7s^2 \)[/tex] completely by identifying and factoring out the greatest common factor (GCF). Here are the step-by-step instructions:
1. Identify the greatest common factor (GCF):
- Look at the coefficients: The GCF of 35 and 7 is 7.
- Look at the variable part: The polynomial involves [tex]\( s^6 \)[/tex] and [tex]\( s^2 \)[/tex]. The smallest power of [tex]\( s \)[/tex] common to both terms is [tex]\( s^2 \)[/tex].
Thus, the GCF of the entire polynomial is [tex]\( 7s^2 \)[/tex].
2. Factor out the GCF:
- Write each term as a product of [tex]\( 7s^2 \)[/tex] and another factor.
We can express each term as follows:
[tex]\[ 35s^6 = 7s^2 \cdot 5s^4 \][/tex]
[tex]\[ 7s^2 = 7s^2 \cdot 1 \][/tex]
3. Rewrite the polynomial: Using the common factor [tex]\( 7s^2 \)[/tex], we can rewrite the polynomial:
[tex]\[ 35s^6 + 7s^2 = 7s^2 (5s^4 + 1) \][/tex]
Therefore, the completely factored form of the polynomial [tex]\( 35s^6 + 7s^2 \)[/tex] is:
[tex]\[ 7s^2 (5s^4 + 1) \][/tex]
1. Identify the greatest common factor (GCF):
- Look at the coefficients: The GCF of 35 and 7 is 7.
- Look at the variable part: The polynomial involves [tex]\( s^6 \)[/tex] and [tex]\( s^2 \)[/tex]. The smallest power of [tex]\( s \)[/tex] common to both terms is [tex]\( s^2 \)[/tex].
Thus, the GCF of the entire polynomial is [tex]\( 7s^2 \)[/tex].
2. Factor out the GCF:
- Write each term as a product of [tex]\( 7s^2 \)[/tex] and another factor.
We can express each term as follows:
[tex]\[ 35s^6 = 7s^2 \cdot 5s^4 \][/tex]
[tex]\[ 7s^2 = 7s^2 \cdot 1 \][/tex]
3. Rewrite the polynomial: Using the common factor [tex]\( 7s^2 \)[/tex], we can rewrite the polynomial:
[tex]\[ 35s^6 + 7s^2 = 7s^2 (5s^4 + 1) \][/tex]
Therefore, the completely factored form of the polynomial [tex]\( 35s^6 + 7s^2 \)[/tex] is:
[tex]\[ 7s^2 (5s^4 + 1) \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.