Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline2h2+11h+92h^2 + 11h + 9

Full solution

Q. Factor.\newline2h2+11h+92h^2 + 11h + 9
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic expression 2h2+11h+92h^2 + 11h + 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 that satisfy these conditions are 22 and 99 because 29=182*9 = 18 and 2+9=112+9 = 11.
  3. Rewrite middle term: Rewrite the middle term 11h11h using the two numbers found in the previous step.\newline2h2+11h+92h^2 + 11h + 9 can be rewritten as 2h2+2h+9h+92h^2 + 2h + 9h + 9.
  4. Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together.\newline(2h2+2h)+(9h+9)(2h^2 + 2h) + (9h + 9)
  5. Factor out common factor: Factor out the greatest common factor from each group. 2h(h+1)+9(h+1)2h(h + 1) + 9(h + 1)
  6. Final factorization: Since both groups contain the common factor (h+1)(h + 1), factor this out.(2h+9)(h+1)(2h + 9)(h + 1)