Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline3u2+7u+43u^2 + 7u + 4

Full solution

Q. Factor.\newline3u2+7u+43u^2 + 7u + 4
  1. Identify Variables: Identify aa, bb, and cc in the quadratic expression 3u2+7u+43u^2 + 7u + 4 by comparing it with the standard form ax2+bx+cax^2 + bx + c.\newlinea=3a = 3\newlineb=7b = 7\newlinec=4c = 4
  2. Find Two Numbers: Find two numbers that multiply to aca*c (which is 34=123*4=12) and add up to bb (which is 77).\newlineThe two numbers that satisfy these conditions are 33 and 44 because:\newline34=123 * 4 = 12\newline3+4=73 + 4 = 7
  3. Rewrite Middle Term: Rewrite the middle term, 7u7u, using the two numbers found in the previous step.\newline3u2+7u+43u^2 + 7u + 4 can be rewritten as 3u2+3u+4u+43u^2 + 3u + 4u + 4.
  4. Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together.\newline(3u2+3u)+(4u+4)(3u^2 + 3u) + (4u + 4)
  5. Factor out Common Factor: Factor out the greatest common factor from each group. 3u(u+1)+4(u+1)3u(u + 1) + 4(u + 1)
  6. Final Factored Form: Since both groups contain the common factor (u+1)(u + 1), factor this out.(3u+4)(u+1)(3u + 4)(u + 1)