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Factor.\newlinen2+7n+10n^2 + 7n + 10

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Q. Factor.\newlinen2+7n+10n^2 + 7n + 10
  1. Identify Coefficients: Identify the coefficients for n2n^2, nn, and the constant term in the quadratic expression n2+7n+10n^2 + 7n + 10. Comparing n2+7n+10n^2 + 7n + 10 with the standard quadratic form ax2+bx+cax^2 + bx + c, we find that a=1a = 1 (coefficient of n2n^2), b=7b = 7 (coefficient of nn), and c=10c = 10 (constant term).
  2. Find Multiplying Numbers: Determine two numbers that multiply to give c(10)c (10) and add up to give b(7)b (7). We are looking for two numbers that when multiplied give 1010 and when added give 77. The numbers 22 and 55 satisfy these conditions because 2×5=102 \times 5 = 10 and 2+5=72 + 5 = 7.
  3. Write Factored Form: Write the factored form using the two numbers found in the previous step.\newlineThe factored form of the quadratic expression is (n+2)(n+5)(n + 2)(n + 5), since these factors will multiply to give the original quadratic expression n2+7n+10n^2 + 7n + 10.