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Factor.\newline2g2+9g+102g^2 + 9g + 10

Full solution

Q. Factor.\newline2g2+9g+102g^2 + 9g + 10
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic expression 2g2+9g+102g^2 + 9g + 10 by comparing it to the standard form ax2+bx+cax^2 + bx + c.a=2a = 2, b=9b = 9, c=10c = 10
  2. Find two numbers: Find two numbers that multiply to aca*c (210=202*10 = 20) and add up to bb (99).\newlineThe numbers 55 and 44 multiply to 2020 and add up to 99.
  3. Rewrite middle term: Rewrite the middle term 9g9g using the two numbers found in the previous step: 5g5g and 4g4g. The expression becomes 2g2+5g+4g+102g^2 + 5g + 4g + 10.
  4. Factor by grouping: Factor by grouping. Group the first two terms and the last two terms separately.\newline(2g2+5g)+(4g+10)(2g^2 + 5g) + (4g + 10)
  5. Factor out common factor: Factor out the greatest common factor from each group. \newlineg(2g+5)+2(2g+5)g(2g + 5) + 2(2g + 5)
  6. Final factorization: Since both groups contain the common factor (2g+5)(2g + 5), factor it out.(g+2)(2g+5)(g + 2)(2g + 5)