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Factor.\newlinew3w2+7w7w^3 - w^2 + 7w - 7

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Q. Factor.\newlinew3w2+7w7w^3 - w^2 + 7w - 7
  1. Identify Common Factors: Look for common factors in pairs of terms. We can try to factor by grouping, which involves combining terms that have common factors. We'll look at the first two terms and the last two terms separately. First pair: w3w2w^3 - w^2 Second pair: 7w77w - 7
  2. Factor by Grouping: Factor out the common factor from the first pair of terms.\newlineThe common factor in w3w^3 and w2w^2 is w2w^2.\newlinew3w2=w2(w1)w^3 - w^2 = w^2(w - 1)
  3. Factor First Pair: Factor out the common factor from the second pair of terms.\newlineThe common factor in 7w7w and 7-7 is 77.\newline7w7=7(w1)7w - 7 = 7(w - 1)
  4. Factor Second Pair: Combine the factored pairs.\newlineNow we have:\newlinew2(w1)+7(w1)w^2(w - 1) + 7(w - 1)\newlineNotice that (w1)(w - 1) is a common factor.
  5. Combine Factored Pairs: Factor out the common factor (w1)(w - 1).\newlineWe can now factor (w1)(w - 1) out of both terms.\newlinew2(w1)+7(w1)=(w1)(w2+7)w^2(w - 1) + 7(w - 1) = (w - 1)(w^2 + 7)