Factor. 10u^3 - 20u^2 + 3u - 6 ______

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. For the first two terms, 10u^3 and -20u^2, the common factor is 10u^2. For the last two terms, 3u and -6, the common factor is 3.Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms. 10u^3 - 20u^2 can be factored as 10u^2(u - 2). 3u - 6 can be factored as 3(u - 2).Rewrite Polynomial: Rewrite the polynomial with the factored terms. The polynomial now looks like this: 10u^2(u - 2) + 3(u - 2).Factor Out Binomial Factor: Factor out the common binomial factor (u - 2) from both terms. The polynomial can now be written as (u - 2)(10u^2 + 3).Check for Further Factoring: Check if the second term 10u^2 + 3 can be factored further. Since 10u^2 + 3 has no common factors and is not a difference of squares or a perfect square trinomial, it cannot be factored further.

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10u^3 - 20u^2 + 3u - 6

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. $\newline$ For the first two terms, $10u^3$ and $-20u^2$ , the common factor is $10u^2$ . $\newline$ For the last two terms, $3u$ and $-6$ , the common factor is $3$ .
Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms. $\newline$ $10u^3 - 20u^2$ can be factored as $10u^2(u - 2)$ . $\newline$ $3u - 6$ can be factored as $3(u - 2)$ .
Rewrite Polynomial: Rewrite the polynomial with the factored terms. $\newline$ The polynomial now looks like this: $10u^2(u - 2) + 3(u - 2)$ .
Factor Out Binomial Factor: Factor out the common binomial factor $(u - 2)$ from both terms. $\newline$ The polynomial can now be written as $(u - 2)(10u^2 + 3)$ .
Check for Further Factoring: Check if the second term $10u^2 + 3$ can be factored further. $\newline$ Since $10u^2 + 3$ has no common factors and is not a difference of squares or a perfect square trinomial, it cannot be factored further.