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Factor.\newline14p37p216p+814p^3 - 7p^2 - 16p + 8

Full solution

Q. Factor.\newline14p37p216p+814p^3 - 7p^2 - 16p + 8
  1. Identify Common Factors: Look for common factors in each pair of terms.\newlineWe can factor out 7p27p^2 from the first two terms, 14p314p^3 and 7p2-7p^2.\newline14p37p2=7p2(2p1)14p^3 - 7p^2 = 7p^2(2p - 1)
  2. Factor Out Common Factors: Look for common factors in the last two terms.\newlineWe can factor out 8-8 from the last two terms, 16p-16p and 88.\newline16p+8=8(2p1)-16p + 8 = -8(2p - 1)
  3. Combine Results: Combine the results from Step 11 and Step 22.\newlineWe now have:\newline7p2(2p1)8(2p1)7p^2(2p - 1) - 8(2p - 1)\newlineNotice that (2p1)(2p - 1) is a common factor.
  4. Factor Out Common Factor: Factor out the common factor (2p1)(2p - 1). Factoring (2p1)(2p - 1) out of both expressions gives us: (2p1)(7p28)(2p - 1)(7p^2 - 8)