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Factor.\newline5h2+20h−255h^2 + 20h - 25

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Full solution

Q. Factor.\newline5h2+20h−255h^2 + 20h - 25
  1. Find GCF and Factor: First, look for a greatest common factor (GCF) in all three terms.\newlineGCF of 5h25h^2, 20h20h, and −25-25 is 55.\newlineFactor out the GCF: 5(h2+4h−5)5(h^2 + 4h - 5).
  2. Factor Trinomial: Now, factor the trinomial h2+4h−5h^2 + 4h - 5. We need two numbers that multiply to −5-5 and add to 44. The numbers are 55 and −1-1. Rewrite the middle term using these numbers: h2+5h−h−5h^2 + 5h - h - 5.
  3. Group and Factor: Group the terms: (h2+5h)−(h+5)(h^2 + 5h) - (h + 5).
  4. Factor by Grouping: Factor by grouping.\newlineTake out the common factor hh from the first group: h(h+5)h(h + 5).\newlineThere's a −1-1 common in the second group: −1(h+5)-1(h + 5).\newlineNow we have: h(h+5)−1(h+5)h(h + 5) - 1(h + 5).
  5. Factor Common Binomial: Factor out the common binomial (h+5)(h + 5): (h−1)(h+5)(h - 1)(h + 5).
  6. Final Step: Don't forget the GCF we factored out at the beginning.\newlineMultiply it by the factored form of the trinomial: 5(h−1)(h+5)5(h - 1)(h + 5).

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