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Answer :
To factor the given polynomial expression [tex]\(5x(7x^6 + 8) + 2(7x^6 + 8)\)[/tex], we start by looking for the greatest common factor (GCF) in the expression.
1. Identify the common factor:
The expression consists of two terms: [tex]\(5x(7x^6 + 8)\)[/tex] and [tex]\(2(7x^6 + 8)\)[/tex]. Notice that the expression [tex]\((7x^6 + 8)\)[/tex] appears in both terms. This means [tex]\((7x^6 + 8)\)[/tex] is a common factor of the entire polynomial.
2. Factor out the common factor:
Since [tex]\((7x^6 + 8)\)[/tex] is common to both terms, we can factor it out. This gives:
[tex]\[
(7x^6 + 8)(5x) + (7x^6 + 8)(2)
\][/tex]
When you factor out [tex]\((7x^6 + 8)\)[/tex], the expression inside the parentheses for the factored form will be [tex]\(5x + 2\)[/tex].
3. Write the factored expression:
So, the completely factored form of the polynomial is:
[tex]\[
(5x + 2)(7x^6 + 8)
\][/tex]
By following these steps, the polynomial [tex]\(5x(7x^6 + 8) + 2(7x^6 + 8)\)[/tex] is factored to [tex]\((5x + 2)(7x^6 + 8)\)[/tex].
1. Identify the common factor:
The expression consists of two terms: [tex]\(5x(7x^6 + 8)\)[/tex] and [tex]\(2(7x^6 + 8)\)[/tex]. Notice that the expression [tex]\((7x^6 + 8)\)[/tex] appears in both terms. This means [tex]\((7x^6 + 8)\)[/tex] is a common factor of the entire polynomial.
2. Factor out the common factor:
Since [tex]\((7x^6 + 8)\)[/tex] is common to both terms, we can factor it out. This gives:
[tex]\[
(7x^6 + 8)(5x) + (7x^6 + 8)(2)
\][/tex]
When you factor out [tex]\((7x^6 + 8)\)[/tex], the expression inside the parentheses for the factored form will be [tex]\(5x + 2\)[/tex].
3. Write the factored expression:
So, the completely factored form of the polynomial is:
[tex]\[
(5x + 2)(7x^6 + 8)
\][/tex]
By following these steps, the polynomial [tex]\(5x(7x^6 + 8) + 2(7x^6 + 8)\)[/tex] is factored to [tex]\((5x + 2)(7x^6 + 8)\)[/tex].
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