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Factor.\newline2z2+11z+92z^2 + 11z + 9

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Q. Factor.\newline2z2+11z+92z^2 + 11z + 9
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic expression 2z2+11z+92z^2 + 11z + 9 by comparing it to the standard form ax2+bx+cax^2 + bx + c.a=2a = 2, b=11b = 11, c=9c = 9
  2. Find suitable numbers: Find two numbers that multiply to aca*c (29=182*9 = 18) and add up to bb (1111).\newlineThe numbers 22 and 99 satisfy these conditions because 29=182*9 = 18 and 2+9=112+9 = 11.
  3. Rewrite middle term: Rewrite the middle term 11z11z using the two numbers found in the previous step.\newline2z2+11z+92z^2 + 11z + 9 can be rewritten as 2z2+2z+9z+92z^2 + 2z + 9z + 9.
  4. Factor by grouping: Factor by grouping. Group the first two terms and the last two terms.\newline(2z2+2z)+(9z+9)(2z^2 + 2z) + (9z + 9)
  5. Factor out common factor: Factor out the greatest common factor from each group. 2z(z+1)+9(z+1)2z(z + 1) + 9(z + 1)
  6. Final factorization: Since both groups contain the common factor (z+1)(z + 1), factor it out.(2z+9)(z+1)(2z + 9)(z + 1)