Algebra

Hey guys. Fiell here.. Today, we started our new unit Algebra. We reviewed on factoring polynomials and "Solving by Factoring".

These are the formulas for factoring polynomials:

• for GCE(Greatest common factor)- just factor out the largest visible factor of the expression

ex. 2x ² + 4 >> 2x(x+2)

• for Difference of squares :

ex. x ² -16 >> (x-4)(x+4)

• for difference of cubes:

ex. x ³ -27 >> (x-3)(x ² +3x+9 )

• for sum of cubes:

ex. x ³ +27 >> (x+3)(x ² -3x+9)

• for Trinomial with 1 as leading coeffiecient:

ex. x ² -3x+10
ax ² +bx+c
a=1 b=-3 c=10
sum= -5
product of a*c= 10
possible numbers= (-2,5)
(x-2)(x+5)

• for Trinomial with leading coefficient other that 1:

ex. 4x ² +5x-6
product of a*c=12
possible numbers=(-3,2)>> for product of a and c
(4x-3)(x+2)



Solving by Factoring:
It is basically factoring plus finding the zeroes of x.
ex.

x² + 5x + 6

Factors:
(x + 2)(x + 3)

Set this equal to zero:

(x + 2)(x + 3) = 0

Solve each factor:

x + 2 = 0 or x + 3 = 0
x = –2 or x = – 3

The solution to x² + 5x + 6 = 0 is x = (–3, –2)