Factoring ax2 bx c (PowerPoint)

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```					Factoring ax2 + bx + c, a = 1
April 1st, 2011
Recap
 You have all learned how to multiply binomials.
( x  4)(x  3)

 What pattern do you see?
 Most of the time, NOT ALWAYS, the product is a
…
 Today you are going to learn how to factor
trinomials, when a = ….
 Essentially we will be converting from … form to
… form.
 On Monday we will factor trinomials where a≠1.
Patterns for Expanding & Factoring
 Expand the following and look for a pattern that
would help you go backwards to factored form
from the expanded form.
( x  7)(x  3)                           ...
( x  4)(x  5)                           ...
( x  6)(x  3)                           ...
( x  3)(x  3)                          ...
The two numbers in the brackets, when in factored form, … to give
the … term and … to give the … term in the simplified trinomial.
Factoring a Trinomial, a = 1
 A trinomial is a polynomial with … terms in the
form ax2 + bx + c, where a ≠ 0, b ≠ 0, & c ≠ 0.
 The pattern we discovered showed that to write
in factored form, we are going to be looking for
two integers that multiply to… and add to …
 These two numbers are what end up being …
and … in factored form.
 Note: This pattern only works when a = …!!
 Tomorrow, we will learn a slightly different
method for when a ≠ 1.
Factoring a Trinomial

2 x  10x  12
2               Always check for …
factor first!
 If there are any, factor
them out.
 We are looking for two
numbers that have a
product of … and a sum
of …
 What are the numbers?
…&…
 Check by expanding.
Examples
 Factor the following trinomials.

1)   x  5 x  14
2
2)     x  10 x  25
2

3)   x  5 xy  6 y
2               2        4) 3 x 2 y  9 xy  54 y
Application
 The volume of a cube is given by the
expression 3x  30x  72 cm3. Factor fully to
2

find the expressions for the dimensions of the
cube.

3x 2  30x  72

Therefore, …
Assigned Work

 P.240-241