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

Identify Common Factors: Look for common factors in pairs of terms. We will first look at the terms 2u^3 and -20u^2 to see if there is a common factor. We can factor out 2u^2 from both terms. 2u^3 - 20u^2 = 2u^2(u - 10)Factor Out Common Factors: Look for common factors in the remaining pair of terms. Now we will look at the terms -u and +10 to see if there is a common factor. We can factor out -1 from both terms. -u + 10 = -1(u - 10)Combine Results: Combine the results from Step 1 and Step 2. We have factored out the common factors from each pair of terms: 2u^3 - 20u^2 = 2u^2(u - 10) -u + 10 = -1(u - 10) Now we can write the expression as: 2u^2(u - 10) - 1(u - 10)Factor Out Binomial: Factor out the common binomial factor. We can see that the binomial (u - 10) is common in both terms, so we can factor it out: 2u^2(u - 10) - 1(u - 10) = (u - 10)(2u^2 - 1)

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Q. Factor.

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2u^3 - 20u^2 - u + 10

Identify Common Factors: Look for common factors in pairs of terms. $\newline$ We will first look at the terms $2u^3$ and $-20u^2$ to see if there is a common factor. We can factor out $2u^2$ from both terms. $\newline$ $2u^3 - 20u^2 = 2u^2(u - 10)$
Factor Out Common Factors: Look for common factors in the remaining pair of terms. $\newline$ Now we will look at the terms $-u$ and $+10$ to see if there is a common factor. We can factor out $-1$ from both terms. $\newline$ $-u + 10 = -1(u - 10)$
Combine Results: Combine the results from Step $1$ and Step $2$ . $\newline$ We have factored out the common factors from each pair of terms: $\newline$ $2u^3 - 20u^2 = 2u^2(u - 10)$ $\newline$ $-u + 10 = -1(u - 10)$ $\newline$ Now we can write the expression as: $\newline$ $2u^2(u - 10) - 1(u - 10)$
Factor Out Binomial: Factor out the common binomial factor. $\newline$ We can see that the binomial $(u - 10)$ is common in both terms, so we can factor it out: $\newline$ $2u^2(u - 10) - 1(u - 10) = (u - 10)(2u^2 - 1)$