Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline16t3+8t2+14t+716t^3 + 8t^2 + 14t + 7

Full solution

Q. Factor.\newline16t3+8t2+14t+716t^3 + 8t^2 + 14t + 7
  1. Identify Common Factors: Look for common factors in each pair of terms.\newlineWe can pair the terms as 16t3+8t216t^3 + 8t^2 and 14t+714t + 7 to look for common factors.
  2. Factor Out First Pair: Factor out the common factor from the first pair of terms.\newlineThe common factor in 16t316t^3 and 8t28t^2 is 8t28t^2.\newline16t3+8t2=8t2(2t+1)16t^3 + 8t^2 = 8t^2(2t + 1)
  3. Factor Out Second Pair: Factor out the common factor from the second pair of terms.\newlineThe common factor in 14t14t and 77 is 77.\newline14t+7=7(2t+1)14t + 7 = 7(2t + 1)
  4. Write Down Findings: Write down what we have found so far.\newlineWe have:\newline16t3+8t2=8t2(2t+1)16t^3 + 8t^2 = 8t^2(2t + 1)\newline14t+7=7(2t+1)14t + 7 = 7(2t + 1)\newlineNow we can see that (2t+1)(2t + 1) is a common factor.
  5. Factor Out Common Factor: Factor out the common factor (2t+1)(2t + 1) from the entire expression.\newlineThe polynomial can be written as:\newline16t3+8t2+14t+7=8t2(2t+1)+7(2t+1)16t^3 + 8t^2 + 14t + 7 = 8t^2(2t + 1) + 7(2t + 1)\newline=(8t2+7)(2t+1)= (8t^2 + 7)(2t + 1)