Transcript Factoring Notes

Factoring #4 Warm up
Answers
1) 2x3 + 6x2
• 2x2(x + 3)
2) x2 + 9x + 18
2) (x + 3)(x + 6)
3) x2 -100
3) (x – 10)(x + 10)
4) 3xy – 6x + 8y - 16
4) (y – 2)( 3x + 8)
Factoring: Just the Factors
• What is a factor?
The 2 terms that you would multiply
together to get a third term.
When will I use factoring?
What are factors in numeric
expressions?
When given a polynomial you can
find the factors to assist you in
finding the x intercepts….to come
in the future!
The numbers you multiply
together to get your original
number.
Ex. The number 8 has factors of 1 and 8, or 2 and 4
Factoring: Follow the steps!
Ex. 1) 4x2 + 16x + 16
Hint: ax2 +bx + c
1) Factor out the GCF if possible…….this is a must! 4(x2 + 4x + 4)
2) Write 2 sets of ( ). Put the ax term in the 1st and 3rd
position.
4(x ___)(x ____)
3) Multiply a and c
1 x 4 = 4 write this number down
above the b term.
4) What factors of step 3 add up to the b term?
Insert the correct terms into position 2 and 4
1,4 or 2,2
4(x +2)(x+2)
5) Simplify each set of ( ) if you can.
What happens when the a
coefficient is not 1?
Ex 2) 3b2 + 7b + 2
Done
(3b ___)(3b ___)
Step 1 GCF
Step 2 Two sets of ( )
3*2=6
Factors of 6 are: 1*6, 2*3
(3x + 1)(3x + 6)
(3x + 1)(x + 2)
Step 3 multiply a and c
Step 4 Factors that add to b
put in 2nd and 4th position.
Step 5 Simplify if you can
Ex 3
6x2 – 26x – 20
Nothing different! Just do the steps
2(3x2 – 13x -10) GCF
2(3x ____)(3x ____)
3 x (-10) = - 30
-1,30
-30,1
Two sets of ( ) ax term in 1st and 3rd
Multiply a x c
-2,15
-15,2
-3,10
-10,3
-5,6
-6,5
What factors add up to the b term? Place in 2nd and 4th position
2(3x -15)(3x + 2)
Reduce
2(x-5)(3x+2)
No middle term. Who cares….I
know the steps!
Ex. 4) 2a2 - 8
2(a2 – 4)
GCF
2(a ____)(a ____)
2 sets of ( ) Fill in 1st and 3rd position
1 x -4 = - 4 Multiply a x c
1, -4
zero?
-1,4
2(a + 2)(a – 2)
2, -2
What are factors that add to b term…which is
You Try Some
1) 8y2 + 13y – 6
2) 5x2 + y – 6
3) 3a2 + 14a + 8
Answers
1) (y + 2)(8y – 3)
(5x + 6)(x – 1)
(a + 4)(3a + 2)