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Answer :
To factor the expression [tex]\( 92x^5 + 60x^2 - 16 \)[/tex], follow these steps:
1. Look for Common Factors: Start by identifying any common factors in all the terms. In this case, the coefficients are 92, 60, and -16. The greatest common factor (GCF) of these numbers is 4.
2. Factor Out the GCF: Factor 4 out of each term in the expression:
[tex]\[
92x^5 + 60x^2 - 16 = 4(23x^5 + 15x^2 - 4)
\][/tex]
At this point, the expression inside the parentheses, [tex]\(23x^5 + 15x^2 - 4\)[/tex], does not have any obvious common factors or simple further factors using rational numbers or integers.
3. Check for Further Factorization: The expression inside the parentheses, [tex]\(23x^5 + 15x^2 - 4\)[/tex], involves a higher-degree polynomial which does not lend itself to simple factoring by common factoring techniques directly. Therefore, after factoring out the GCF, we do not have any simpler factorizations based on standard techniques (such as factoring by grouping or special patterns).
Thus, the fully factored form of the polynomial is:
[tex]\[
4(23x^5 + 15x^2 - 4)
\][/tex]
This is the simplest form of factorization for the given expression, considering integer and rational coefficients.
1. Look for Common Factors: Start by identifying any common factors in all the terms. In this case, the coefficients are 92, 60, and -16. The greatest common factor (GCF) of these numbers is 4.
2. Factor Out the GCF: Factor 4 out of each term in the expression:
[tex]\[
92x^5 + 60x^2 - 16 = 4(23x^5 + 15x^2 - 4)
\][/tex]
At this point, the expression inside the parentheses, [tex]\(23x^5 + 15x^2 - 4\)[/tex], does not have any obvious common factors or simple further factors using rational numbers or integers.
3. Check for Further Factorization: The expression inside the parentheses, [tex]\(23x^5 + 15x^2 - 4\)[/tex], involves a higher-degree polynomial which does not lend itself to simple factoring by common factoring techniques directly. Therefore, after factoring out the GCF, we do not have any simpler factorizations based on standard techniques (such as factoring by grouping or special patterns).
Thus, the fully factored form of the polynomial is:
[tex]\[
4(23x^5 + 15x^2 - 4)
\][/tex]
This is the simplest form of factorization for the given expression, considering integer and rational coefficients.
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