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How Do You Find All the Possible Factors of a Trinomial?

Find the possible factors of 6x2+19x+15

Summary

  1. To figure out the template, look at the signs of the trinomial
  2. Since both signs are positive, our binomials will both have PLUS signs
  3. The factors of 6, 1•6 and 2•3, will be the coefficients of our first terms
  4. The factors of 15, 1•15 and 3•5, will be our second terms
  5. Now just list all the possible combinations of the factors

Notes

    1. We need to look at the signs of our trinomial to determine the template
    1. Our last sign is an ADDITION sign
    1. If the sign on the trinomial we're factoring is POSITIVE, the two binomials we get when we factor will have the SAME SIGNS
    1. Our first sign is also an ADDITION sign
    1. Since both of our signs are POSITIVE, we'll have two binomials with ADDITION signs
    1. Since both of our signs are POSITIVE, we'll have two binomials with ADDITION signs
    1. The factors of 6 will be the coefficients of the first terms of the binomials when we factor
    2. 6 factors into 1•6 and 2•3
    1. These will be the possible coefficients of the first terms of our new binomials
    1. The factors of 15 will be the coefficients of the second terms of the binomials when we factor
    2. 15 factors into 1•15 and 3•5
    1. These will be the possible coefficients of the second terms of our new binomials
    1. Remember, 6 factored into 1•6 and 2•3
    1. Remember, 6 factored into 1•6 and 2•3
    1. x is the variable we had in our original trinomial
    2. 1 and 6, our first set of factors, become the coefficients of the first terms
    1. This was the template we figured out before
    1. Remember, 15 factored into 1•15 and 3•5
    2. These will be the second terms of our binomials
    1. Remember, 15 factored into 1•15 and 3•5
    2. These will be the second terms of our binomials
    1. Remember, we're looking for ALL the possible combinations
    2. So if we flip the 1 and the 15, we'll have a different pair of binomials
    1. 15 also factored into 3 and 5
    1. So 3 and 5 could also be our second terms
    1. Remember, we're looking for ALL possible combinations
    2. So we can switch the second terms to get a new pair of binomials
    1. Remember, 6 also factored into 2 and 3
    2. So 2 and 3 could also be the coefficients of our first terms
    3. This means we have another set of binomials we need to look at
    1. This time, 2 and 3 will be our coefficients
    1. 2 and 3 are our coefficients
    2. We still have x as our variable
    1. We need to find all the possible combinations of binomials, with the factors of 15 as our second terms
    2. Just like before, we'll use 1 and 15 and 3 and 5 for our second terms
    1. Remember, we still want to find ALL the possible combinations
    2. So make sure you flip the last terms as well!