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Factor.\newlineq2+14q+13q^2 + 14q + 13

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Q. Factor.\newlineq2+14q+13q^2 + 14q + 13
  1. Identify aa, bb, cc: Identify aa, bb, and cc in the quadratic expression q2+14q+13q^2 + 14q + 13.\newlineThe quadratic expression is in the standard form aq2+bq+caq^2 + bq + c, where a=1a = 1, b=14b = 14, and bb00.
  2. Find two numbers: Find two numbers that multiply to cc (1313) and add up to bb (1414).\newlineWe are looking for two numbers that when multiplied give 1313 and when added give 1414. The numbers 11 and 1313 satisfy these conditions because:\newline1×13=131 \times 13 = 13 (product is cc)\newline131300 (sum is bb)
  3. Write factored form: Write the factored form using the two numbers found in Step 22.\newlineThe factored form of the quadratic expression is (q+1)(q+13)(q + 1)(q + 13), because:\newline(q+1)(q+13)=q2+13q+1q+13=q2+14q+13(q + 1)(q + 13) = q^2 + 13q + 1q + 13 = q^2 + 14q + 13