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Factor the quadratic expression x2+9x+20x^2+9x+20

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Q. Factor the quadratic expression x2+9x+20x^2+9x+20
  1. Identify Coefficients: Identify the coefficients aa, bb, and cc in the quadratic expression x2+9x+20x^2 + 9x + 20. The quadratic expression is in the form ax2+bx+cax^2 + bx + c, where a=1a = 1, b=9b = 9, and c=20c = 20.
  2. Find Multiplying Numbers: Find two numbers that multiply to cc (which is 2020) and add up to bb (which is 99).\newlineThe two numbers that satisfy these conditions are 44 and 55, because 4×5=204 \times 5 = 20 and 4+5=94 + 5 = 9.
  3. Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step.\newlineThe factored form is (x+4)(x+5)(x + 4)(x + 5), because when expanded, (x+4)(x+5)(x + 4)(x + 5) gives x2+4x+5x+20x^2 + 4x + 5x + 20, which simplifies to x2+9x+20x^2 + 9x + 20.