Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor.\newline10t315t2+6t910t^3 - 15t^2 + 6t - 9

Full solution

Q. Factor.\newline10t315t2+6t910t^3 - 15t^2 + 6t - 9
  1. Identify Common Factors: Look for common factors in the first two terms and the last two terms separately.\newlineFor the first two terms, 10t310t^3 and 15t2-15t^2, the common factor is 5t25t^2.\newlineFor the last two terms, 6t6t and 9-9, the common factor is 33.
  2. Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms.\newline10t315t2=5t2(2t3)10t^3 - 15t^2 = 5t^2(2t - 3)\newline6t9=3(2t3)6t - 9 = 3(2t - 3)
  3. Rewrite Using Factored Terms: Now, we have the expression in the form of two binomials that share a common factor of (2t3)(2t - 3). Rewrite the expression using the factored terms. 10t315t2+6t9=5t2(2t3)+3(2t3)10t^3 - 15t^2 + 6t - 9 = 5t^2(2t - 3) + 3(2t - 3)
  4. Factor Out Common Binomial Factor: Factor out the common binomial factor (2t3)(2t - 3) from both terms.\newline5t2(2t3)+3(2t3)=(5t2+3)(2t3)5t^2(2t - 3) + 3(2t - 3) = (5t^2 + 3)(2t - 3)