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Factor.\newlinez2+10z+21z^2 + 10z + 21

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Q. Factor.\newlinez2+10z+21z^2 + 10z + 21
  1. Identify Coefficients: Identify the coefficients of the quadratic expression.\newlineThe quadratic expression is z2+10z+21z^2 + 10z + 21. In the standard form of a quadratic expression, ax2+bx+cax^2 + bx + c, the coefficient aa is the coefficient of z2z^2, which is 11. The coefficient bb is the coefficient of zz, which is 1010. The coefficient cc is the constant term, which is 2121.
  2. Find Multiplying Numbers: Find two numbers that multiply to cc (2121) and add up to bb (1010). We need to find two numbers that multiply to 2121 and add up to 1010. The numbers 33 and 77 satisfy these conditions because 3×7=213 \times 7 = 21 and 3+7=103 + 7 = 10.
  3. Write Factored Form: Write the factored form using the two numbers found.\newlineThe factored form of the quadratic expression is (z+3)(z+7)(z + 3)(z + 7), because when we expand this, we get z2+3z+7z+21z^2 + 3z + 7z + 21, which simplifies to z2+10z+21z^2 + 10z + 21.