Question 449383
how do you factor 4x^2=4x+5?
---
Rearrange:
4x^2 - 4x - 5 = 0
----
Using the quadratic formula:
x = [4 +- sqrt(16-4*4*-5)]/(2*4)
---------------------
x = [4 +- sqrt(96)]/8
-----
x = [4 +- 4sqrt(6)]/8
----
r1 = (1/2)+(1/2)sqrt(6) or r2 = (1/2)-(1/2)sqrt(6)
-----
Each of these is a root of the quadratic.
---
The factored form would be (x-r1)(x-r2) = 0
===============================================
So the quadratic formula can ALWAYS be used to factor
a quadratic polynomial.
===============================================
If you are familiar with FOIL, Inverse FOIL can
be used to factor some quadratics.
----
Example:
 2x^2+7x-15 = 0
ac = 2*-15 = -30
b = 7
----
Think of 2 numbers whose product is ac and whose sum is b:
ac = 10*-3 = -30
b = 10+ -3 = 7
-----
Rewrite the quadratic replacing the "b-term":
2x^2 + 10x-3x -15 = 0
-----
Factor the 1st two and the last two terms separately:
2x(x+5)-3(x+5) = 0
Factor again:
(x+5)(2x-3) = 0
=============================
Cheers,
Stan H.
=============================