Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline2k2+9k+72k^2 + 9k + 7

Full solution

Q. Factor.\newline2k2+9k+72k^2 + 9k + 7
  1. Identify aa, bb, cc: Identify aa, bb, and cc in the quadratic expression 2k2+9k+72k^2 + 9k + 7. Compare 2k2+9k+72k^2 + 9k + 7 with ax2+bx+cax^2 + bx + c. a=2a = 2 bb00 bb11
  2. Find Multiplying Numbers: Find two numbers that multiply to aca*c (which is 27=142*7=14) and add up to bb (which is 99).\newlineWe need to find two numbers that satisfy these conditions.\newlineAfter checking possible pairs that multiply to 1414 (11 and 1414, 22 and 77), we see that none of these pairs add up to 99.\newlineThis means we cannot factor the quadratic expression by simple inspection or by using integer pairs.
  3. Quadratic Formula or Completing Square: Since the quadratic expression cannot be factored using integer pairs, we will attempt to factor it using the quadratic formula or completing the square. However, since the original question prompt asks for factoring, we must conclude that the quadratic expression 2k2+9k+72k^2 + 9k + 7 cannot be factored over the integers.