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← Add to B - College Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. So far, we've been dealing with quadratic polynomials, like x squared plus 5 x
  2. plus 6, to figure out how to factor this. We've been looking for two numbers
  3. that add to equal the middle term coefficient, and multiply to equal the final
  4. coefficient. So, in the case of this polynomial, we end up with 2 and 3 as our
  5. two coefficients. What if I told you, though, that this quantity a,b, in other
  6. words, the product of the two numbers that add to equal the middle coefficient,
  7. is also equal to the product of two coefficients from the original expression.
  8. Let's just play around with this for a second, though. I'm going to name each of
  9. the coefficients of each term in this three term expression A, B, and C. So, A
  10. in this case is 1, B is 5, and C is 6. So before we found the two numbers that
  11. add to equal this term, they were 2 and 3. But what if I told you that these
  12. multiply to equal not just this final term, but actually the product of two of
  13. the coefficients in this expression over here. So the two numbers we found to
  14. equal this coefficient B, multiply to equal what? Do they multiply to equal A
  15. squared, B squared, C squared, AB, BC, or AC?