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Factor.\newlinez2+13z+22z^2 + 13z + 22\newline______

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Q. Factor.\newlinez2+13z+22z^2 + 13z + 22\newline______
  1. Identify Coefficients: Identify the coefficients of the quadratic expression.\newlineThe quadratic expression is z2+13z+22z^2 + 13z + 22. Here, the coefficient of z2z^2 (a)(a) is 11, the coefficient of zz (b)(b) is 1313, and the constant term (c)(c) is 2222.
  2. Find Two Numbers: Find two numbers that multiply to give the constant term cc and add up to the coefficient of zz (bb).\newlineWe need to find two numbers whose product is 2222 (the constant term) and whose sum is 1313 (the coefficient of zz). The numbers 22 and 1111 satisfy these conditions because 2×11=222 \times 11 = 22 and 2+11=132 + 11 = 13.
  3. Write Factored Form: Write the factored form using the two numbers found in the previous step.\newlineThe factored form of the quadratic expression z2+13z+22z^2 + 13z + 22 is (z+2)(z+11)(z + 2)(z + 11), since these factors will multiply out to the original quadratic expression.

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