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Factor.\newlineq2+4q+3q^2 + 4q + 3

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Q. Factor.\newlineq2+4q+3q^2 + 4q + 3
  1. Identify Variables: Identify aa, bb, and cc in the quadratic expression q2+4q+3q^2 + 4q + 3. Compare q2+4q+3q^2 + 4q + 3 with the standard quadratic form ax2+bx+cax^2 + bx + c. Here, a=1a = 1, b=4b = 4, and c=3c = 3.
  2. Find Numbers: Find two numbers that multiply to cc (which is 33) and add up to bb (which is 44).\newlineThe numbers that satisfy these conditions are 11 and 33 because:\newline1×3=31 \times 3 = 3 (product equals cc)\newline1+3=41 + 3 = 4 (sum equals 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+3)(q + 1)(q + 3).