Teacher2Teacher

Q&A #104

Teachers' Lounge Discussion: Factoring trinomials

T2T || FAQ || Ask T2T || Teachers' Lounge || Browse || Search || T2T Associates || About T2T

View entire discussion
[<< prev] [ next >>]

From: Daniel Springer

To: Teacher2Teacher Public Discussion
Date: 2009020320:44:24
Subject: trinomial factoring redered trivial by simple method (Can even be done mentally)

I have never seen this in Mathematics Teacher or any other source. The method renders mentally solving (or factoring) reasonable quadratics nearly trival. EXAMPLE: If, 20x^2 + 28x - 3 = 0 THINK: "product = 60, differ by 28, want smaller number" AHA! "2 and 30" Thus, x = 2/20 or -30/20 DONE! In general, if ax^2 + bx + c = 0, a is positive Then, ax(ax + b) = -c We think of a pair of numbers that differ by b whose product is -c, lets say the pair is {P, Q}, then {-P, -Q} also satisfy the equation. We decide if ax is larger or smaller than (ax + b). This is easy, if b > 0 then ax is smaller, otherwise ax is larger. Suppose that ax is smaller and P is the smaller number, then Then, our answer is: x = P/a or x = -Q/a

Post a reply to this message
Post a related public discussion message
Ask Teacher2Teacher a new question


[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || The Math Library || Quick Reference || Math Forum Search
_____________________________________

Teacher2Teacher - T2T ®
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/