Factor. 2r^3 - r^2 + 20r - 10 ______

Grouping Terms: Group terms to make factoring easier. We can group the terms as follows: (2r^3 - r^2) + (20r - 10).Factor Out Common Factors: Factor out the greatest common factor from each group. From the first group (2r^3 - r^2), we can factor out r^2, giving us r^2(2r - 1). From the second group (20r - 10), we can factor out 10, giving us 10(2r - 1).Identify Common Factor: Notice that both groups now have a common factor of (2r - 1). We can factor out (2r - 1) from the entire expression. This gives us (2r - 1)(r^2 + 10).Check Factored Form: Check the factored form by expanding it to ensure it matches the original polynomial. (2r - 1)(r^2 + 10) = 2r^3 + 20r - r^2 - 10 = 2r^3 - r^2 + 20r - 10. The expanded form matches the original polynomial, so the factoring is correct.

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Q. Factor.

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2r^3 - r^2 + 20r - 10

Grouping Terms: Group terms to make factoring easier. $\newline$ We can group the terms as follows: $2r^3 - r^2$ + $20r - 10$ .
Factor Out Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group $2r^3 - r^2$ , we can factor out $r^2$ , giving us $r^2(2r - 1)$ . $\newline$ From the second group $20r - 10$ , we can factor out $10$ , giving us $10(2r - 1)$ .
Identify Common Factor: Notice that both groups now have a common factor of $(2r - 1)$ . $\newline$ We can factor out $(2r - 1)$ from the entire expression. $\newline$ This gives us $(2r - 1)(r^2 + 10)$ .
Check Factored Form: Check the factored form by expanding it to ensure it matches the original polynomial. $\newline$ $(2r - 1)(r^2 + 10) = 2r^3 + 20r - r^2 - 10 = 2r^3 - r^2 + 20r - 10$ . $\newline$ The expanded form matches the original polynomial, so the factoring is correct.