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Learn Alegebra 1
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BY CALEB REAGOR, BRENDAN INSON, AND JACK GUENTHER
FLUGENHEIMAN( N E E D H E L P ? L O O K A T V O C A B U L A R Y A T V E R Y E N D )
Chapter 6 Tutorial
Chapter Opener
http://algebraiperiod6.pbworks.com/Flugenheiman-Chapter-6-Opener
Section 6.1
http://algebraiperiod6.pbworks.com/Flugenheiman-Section-1
Section 6.2
In this section you will learn how to factor trinomials with the form of x²+bx+c
The coefficient will only be 1 for the squared variable
Section 6.2
You may remember that factoring is writing a product into factors
For example the factors of x²+3x+2 are (x+1) and (x+2)
x times x equals x² and it can not be x² and 1 because that would get rid of the 3x in the middle
There is 3x+2 because positive factors of two are 2 and 1 and the sum of them is 3 for the 3x
Section 6.2
Practice ProblemsFactor two binomials out of the problemsx²+7x+10x²+8x+12
Section 6.2
Answers(x+5)(x+2)(x+2)(x+6)
Section 6.2
There are negatives such as:x²-3x+2=(x-2)(x-1)x²+1x-2=(x-1)(x+2)x²-1x-2=(x+1)(x-2)There are some times perfect square
trinomialsx²+2x+1=(x+1)(x+1)=(x+1) ²
Section 6.2
Practice problemsx²-3x+2x²+3x-18x²-3x-18x²+6x+9
Section 6.2
Answers(x-2)(x-1)(x+6)(x-3)(x+3)(x-6)(x+3) ²
Section 6.2
There are also ones with the fourth powerx⁴+3x²+2=(x²+2)(x²+1)There are also ones with two variablesx²+2xy+y²=(x+y)(x+y) or (x+y)²
Section 6.2
Practice Problemsx⁴+2x²+1x²+4xy+2y²
Section 6.2
Answers(x²+1) ²(x+2y) ²
Section 6.4
In this section you will learn how to factor binomials of the form ax²+bx+c by grouping
Section 6.4
Go back to section 6.1 for the basics of factoring ax ²+bx+c with “a”=1
This section is an extended method of this but to have “a” larger then 1
An example of this is 6x²+11x+3Before you start you always need to see if it is
a perfect square trinomial or if it has a greatest common factor- this problem has none
Section 6.4
This is how to solve 6x ²+11x+3To solve the problem you multiply 6x ² and 3
to equal 18x²You then find factors of 18x² that equal 11x9x plus 2x equals 11x; when multiplied, they
equal 18x²
Section 6.4
You take those factors and put it into the equationSo instead of 6x ²+11x+3 you do 6x²+9x+2x+3You then group them into groups with greatest
common factors; (6x²+9x)+(2x+3)Then you factor out the greatest common factors
of the grouped parts, try to make the inside problem the same, for example
(6x ²+9x)+(2x+3)=3x(2x+3)+1(2x+3)You then add/subtract the greatest common
factors; you then multiply that equation by the other same terms (3x+1)(2x+3)
Section 6.4
Practice Problems10x²+21x+26x²+32x+107x²+17x+6
Section 6.4
Answers10x²+20x+x+2=(10x²+20x)+
(x+2)=10x(x+2)+1(x+2) finally equaling (10x+1)(x+2)
2(gcf)(3x²+15x+x+5)=2(3x²+x)+(15x+5)=2[x(3x+1)+5(3x+1)] finally equaling 2(x+5)
(3x+1)7x²+14x+3x+6=(7x²+14x)
+(3x+6)=7x(x+2)+3(x+2) finally equaling (7x+3)(x+2)
Section 6.4
You can do this for perfect square trinomials and negative problems such as
4x²-8x+4=(2x-2)² since that this is a prime you do not have to do all of the work
ax²+bx-c in this you do the same thing you do for a positive number but the final equation looks like this (dx+e)(fx-g) and that is the same for ax²-bx-c but the negative number without a variable is larger then the positive
Section 6.4
Practice Problems9x²+12x+48x²+63x-88x²-63x-8
Section 6.4
Answers(3x+2)²(8x-1)(x+8)(8x+1)(x-8)
Vocabulary
http://algebraiperiod6.pbworks.com/Flugenheiman-Vocabulary
