factoring trinomials x2 + bx + c
from book chapter  4.4 p. 356

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PART 1 : LECTURE

example1
So far you learnt how to expand (x+2)(x+3) using FOIL
= x2 + 5x + 6
Now we need to work the process backard. To go from   x2 + 5x + 6       to the factor form (x+2) (x+ 3)
Notice that the first term = x2  is easily found by multiplying x by x (First terms)
The last term is found by find 2 factors of 6 like 2 and 3.
The middle term is found by adding the inside and outside  terms 2x + 3x

So let's say you want to factor x2 + 5x + 6
step 1) first write the skeleton: (x       )  ( x         )
step 2) Notice that the last term is positive so the terms need to have the same sign.
But because the middle term is positive, then the 2 factors has to be positive
(x +       ) ( x +       )
step3) Find 2 factors of 6.    
6 = 2 x 3 or 6 = 1 x 6
step3) Check the middle term to find the correct factor form.
(x+1 ) (x+ 6)   middle term = x + 6x = 7x    not correct
(x + 2 ) ( x+ 3) middle term = 2x + 3x = 5x.   GOOD!

example2

Factor : x2  - 8x + 12
Note that the middle term is negative and that the last term is positive. So the skeleton is: (x -         ) ( x -     )

example3

Factor x2 - 7x + 12
skeleton (x -  ) ( x -   )

example4

Factor x2 + x - 6
Note that the last term is negative. So the 2 factors of 6 don't have the same sign. The skeleton is: (x -   ) (x +   )

example5

Factor x2 -4x - 12
(x -   ) ( x +    )

example6

Factor x2 - 5x - 24

example7

Factor x2 + 20x + 36

example8

x2 + 6xy -16 y2

example9

y2 + 4yz - 60 z2

example10

3x2 +21x + 30

example11

x4y2 + 3x3y3 + 2 x2 y4

Study the examples in your book p. 357

PART II - QUIZ

from assignments due today

PART III assignments for next time.

Study examples from your book p. 357
p.360 6, 9, 11, 12, 15, 20, 30

 

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