Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline4g2+7g+34g^2 + 7g + 3

Full solution

Q. Factor.\newline4g2+7g+34g^2 + 7g + 3
  1. Identify aa, bb, cc: Identify aa, bb, and cc in the quadratic expression 4g2+7g+34g^2 + 7g + 3 by comparing it with the standard form ax2+bx+cax^2 + bx + c.
    a=4a = 4
    b=7b = 7
    bb00
  2. Find Numbers Multiply Add: Find two numbers that multiply to aca*c (which is 43=124*3=12) and add up to bb (which is 77).\newlineThe numbers that satisfy these conditions are 44 and 33 because:\newline4×3=124 \times 3 = 12\newline4+3=74 + 3 = 7
  3. Rewrite Middle Term: Rewrite the middle term, 7g7g, using the two numbers found in the previous step.\newline4g2+7g+34g^2 + 7g + 3 can be rewritten as 4g2+4g+3g+34g^2 + 4g + 3g + 3.
  4. Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together.\newline(4g2+4g)+(3g+3)(4g^2 + 4g) + (3g + 3)
  5. Factor out Common Factor: Factor out the common factor from each group. 4g(g+1)+3(g+1)4g(g + 1) + 3(g + 1)
  6. Factor Out Groups: Since both groups contain the common factor (g+1)(g + 1), factor this out.(4g+3)(g+1)(4g + 3)(g + 1)