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Factor.\newline16p38p214p+716p^3 - 8p^2 - 14p + 7

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Q. Factor.\newline16p38p214p+716p^3 - 8p^2 - 14p + 7
  1. Identify Common Factor: Look for a common factor in all terms.\newlineCheck if there is a common factor that can be factored out from all terms of the polynomial 16p38p214p+716p^3 - 8p^2 - 14p + 7.\newlineThere is no common factor in all terms.
  2. Group Terms: Group terms to facilitate factoring by grouping.\newlineGroup the terms into two pairs: 16p38p216p^3 - 8p^2 and 14p+7 -14p + 7.
  3. Factor First Group: Factor out the common factor from the first group.\newlineFactor out the greatest common factor, which is 8p28p^2, from the first group (16p38p2)(16p^3 - 8p^2).\newline8p2(2p1)8p^2(2p - 1)
  4. Factor Second Group: Factor out the common factor from the second group.\newlineFactor out the greatest common factor, which is 7-7, from the second group (14p+7)(-14p + 7).\newline7(2p1)-7(2p - 1)
  5. Write Factored Form: Write the factored form of the polynomial.\newlineNotice that both groups now have a common binomial factor (2p1)(2p - 1).\newlineCombine the factored groups using the common binomial factor.\newlineFactored form: (8p27)(2p1)(8p^2 - 7)(2p - 1)