Factor completely. 20f^(3)-10f^(2)+2f-1

Grouping for Factoring: Group the terms in pairs to prepare for factoring by grouping. Group the first two terms and the last two terms together. (20f^3 - 10f^2) + (2f - 1)Factor Out GCF: Factor out the greatest common factor (GCF) from each group. From the first group, the GCF is 10f^2, and from the second group, the GCF is 1. 10f^2(2f - 1) + 1(2f - 1)Check Common Terms: Check if the terms in parentheses are the same. Both groups have the term (2f - 1), which means we can factor this term out. (2f - 1)(10f^2 + 1)Verify Further Factoring: Verify if the expression can be factored further. The term 10f^2 + 1 is a sum of squares and cannot be factored further using real numbers. The expression is now fully factored.

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Factor completely. $\newline$ $20 f^{3}-10 f^{2}+2 f-1$

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Math Problems

Algebra 2

Multiply and divide rational expressions

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Q. Factor completely.

\newline

20 f^{3}-10 f^{2}+2 f-1

Grouping for Factoring: Group the terms in pairs to prepare for factoring by grouping. Group the first two terms and the last two terms together. $20f^3 - 10f^2$ + $2f - 1$
Factor Out GCF: Factor out the greatest common factor (GCF) from each group. $\newline$ From the first group, the GCF is $10f^2$ , and from the second group, the GCF is $1$ . $\newline$ $10f^2(2f - 1) + 1(2f - 1)$
Check Common Terms: Check if the terms in parentheses are the same. $\newline$ Both groups have the term $(2f - 1)$ , which means we can factor this term out. $\newline$ $(2f - 1)(10f^2 + 1)$
Verify Further Factoring: Verify if the expression can be factored further. $\newline$ The term $10f^2 + 1$ is a sum of squares and cannot be factored further using real numbers. $\newline$ The expression is now fully factored.