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How Do You Find a Missing Term in a Polynomial?

Find all integer values of k so the trinomial, x2+kx+10, can be factored.

Summary

  1. Looking at the last sign in our trinomial shows us that our factorization could have either both positive or both negative signs
  2. The factors of 10 are the only possible values for the second terms of our binomials
  3. We can either have 1 and 10, or 2 and 5 as the second terms for a single pair of binomials
  4. FOIL the binomial pairs to find the possible values of k

Notes

    1. Since 'k' could be positive or negative, the first sign of the trinomial could be positive or negative
    1. Since the second sign in our trinomial is positive we know that the signs of our binomials will be the same
    2. But because 'k' could be positive or negative, we need to check both possibilities for the signs of our binomials
    1. The factors of 10 come in pairs and are 1•10 and 2•5