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Factor.\newline6u39u2+2u36u^3 - 9u^2 + 2u - 3

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Q. Factor.\newline6u39u2+2u36u^3 - 9u^2 + 2u - 3
  1. Identify Common Factors: Look for common factors in pairs of terms. We will first look at the pairs of terms separately to see if there is a common factor in any of the pairs. We will start with the first two terms, 6u36u^3 and 9u2-9u^2, and then the last two terms, 2u2u and 3-3. For the first pair, the common factor is 3u23u^2, and for the second pair, the common factor is 11 (since 22 and 33 are prime numbers and do not share a common factor other than 11).
  2. Factor Out Common Factors: Factor out the common factors from each pair.\newlineNow we will factor out the common factors from each pair.\newlineFor the first pair, 6u39u26u^3 - 9u^2, we factor out 3u23u^2:\newline3u2(2u3)3u^2(2u - 3)\newlineFor the second pair, 2u32u - 3, we cannot factor out anything other than 11, so it remains the same:\newline1(2u3)1(2u - 3)
  3. Find Common Binomial Factor: Look for a common binomial factor.\newlineNow we will look for a common binomial factor from the two results we got from step 22. We notice that both terms have a common binomial factor of (2u3)(2u - 3).
  4. Factor Out Binomial Factor: Factor out the common binomial factor.\newlineWe will now factor out the common binomial factor (2u3)(2u - 3) from both terms.\newline(3u2)(2u3)+(1)(2u3)(3u^2)(2u - 3) + (1)(2u - 3)\newlineThis gives us:\newline(2u3)(3u2+1)(2u - 3)(3u^2 + 1)