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Factor.\newline2s2−48s+462s^2 - 48s + 46

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Full solution

Q. Factor.\newline2s2−48s+462s^2 - 48s + 46
  1. Identify Quadratic Trinomial Form: Identify the form of the quadratic trinomial, which is ax2+bx+cax^2 + bx + c.
  2. Find Multiplying and Adding Numbers: Look for two numbers that multiply to 2×462 \times 46 (which is 9292) and add up to −48-48.
  3. Use Numbers to Rewrite Middle Term: The numbers that work are −2-2 and −46-46 because −2×−46=92-2 \times -46 = 92 and −2−46=−48-2 - 46 = -48.
  4. Factor by Grouping: Rewrite the middle term using the numbers found: 2s2−2s−46s+462s^2 - 2s - 46s + 46.
  5. Factor Out Common Factors: Factor by grouping: (2s2−2s)−(46s−46)(2s^2 - 2s) - (46s - 46).
  6. Factor Out Common Binomial: Factor out the common factors in each group: 2s(s−1)−46(s−1)2s(s - 1) - 46(s - 1).
  7. Identify Mistake in Factoring: Factor out the common binomial (s−1)(s - 1): (2s−46)(s−1)(2s - 46)(s - 1).
  8. Identify Mistake in Factoring: Factor out the common binomial (s−1)(s - 1): (2s−46)(s−1)(2s - 46)(s - 1).Realize there's a mistake because 2s−462s - 46 doesn't factor out of the original expression correctly.

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