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Factor.\newline2p3p2+16p82p^3 - p^2 + 16p - 8

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Q. Factor.\newline2p3p2+16p82p^3 - p^2 + 16p - 8
  1. Look for common factors: Look for common factors in pairs of terms.\newlineWe 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.
  2. Factor out greatest common factor: Factor out the greatest common factor from the first two terms.\newlineThe greatest common factor of 2p32p^3 and p2-p^2 is p2p^2. So we factor p2p^2 out of those terms.\newline2p3p2=p2(2p1)2p^3 - p^2 = p^2(2p - 1)
  3. Factor out greatest common factor: Factor out the greatest common factor from the last two terms.\newlineThe greatest common factor of 16p16p and 8-8 is 88. So we factor 88 out of those terms.\newline16p8=8(2p1)16p - 8 = 8(2p - 1)
  4. Write with factored groups: Write the expression with the factored groups.\newlineNow we have factored the polynomial into two groups:\newlinep2(2p1)+8(2p1)p^2(2p - 1) + 8(2p - 1)
  5. Factor out common binomial factor: Factor out the common binomial factor.\newlineWe can see that the binomial (2p1)(2p - 1) is common in both terms, so we can factor it out.\newlineThe factored form is (2p1)(p2+8)(2p - 1)(p^2 + 8).