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Factor.\newlinev2+8v+15v^2 + 8v + 15

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Q. Factor.\newlinev2+8v+15v^2 + 8v + 15
  1. Identify Coefficients: Identify the coefficients of the quadratic expression.\newlineThe quadratic expression is v2+8v+15v^2 + 8v + 15. Here, the coefficient of v2v^2 (aa) is 11, the coefficient of vv (bb) is 88, and the constant term (cc) is 1515.
  2. Find Multiplying Numbers: Find two numbers that multiply to c(15)c (15) and add up to b(8)b (8).\newlineWe need to find two numbers that multiply together to give 1515 and add together to give 88. The numbers 33 and 55 satisfy these conditions because 3×5=153 \times 5 = 15 and 3+5=83 + 5 = 8.
  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 (v+3)(v+5)(v + 3)(v + 5), because when we expand this, we get v2+3v+5v+15v^2 + 3v + 5v + 15, which simplifies to v2+8v+15v^2 + 8v + 15.