Download NRF 10 - Quiz 2 – Supplemental Support Notes Multiplying

NRF 10 - Quiz 2 – Supplemental Support Notes
Multiplying Binomials using FOIL
Example:
(2x+3)(3x-2) = 6x2 – 4x + 9x – 6
F
O
I
L
6x2 + 5x – 6
Factoring Polynomials
Step 1 – Make sure the polynomial is in simplified form (collect like terms)
Step 2 – Determine the GCF of the terms
Step 3 – If the GCF is not 1, then factor the GCF out of each term
Step 4 – look at what remains(in the brackets). Check to see if it can
be factored further into (a+b)(c+d) form or as a
Difference of Squares (a-b)(a+b)
Find the GCF
3
2
3
2
Example:
3x +6x +x +10x + 12x
4x3 = 2*2*x*x*x
3
2
4x +16x +12x
16x = 2*2*2*2*x
2
4x(x + 4x + 3)
12x = 2*2*3*x
4x(x + 1)(x+3) Factored Form
GCF = 2*2*x = 4x
Factoring by Decomposition: 6x2 + 5x – 6
Step 1 – Multiply the a and c terms
6 x -6 = -36
Step 2 – determine two numbers with a product equaling a X c with a sum of b
Sum (+5) Product (-36)
-6 , 6
4 , -9
+5
9, -4
The numbers are +9 and -4
Step 3 – decompose the middle term of the trinomial using the two numbers
6x2 -4x + 9x – 6
Step 4 – Factor out the GCF of the 1st two terms and of the 2nd two terms
6x2 – 2*3*x*x
4x - 2*2*x
GCF = 2x
9x – 3*3*x
6 - 2*3
GCF = 3
2x(3x -2) +3(3x – 2)
Step 5 – factor the resulting expression
(3x-2)(2x+3)
Difference of Squares
A difference of squares is a binomial in the form a2 – b2.
In its factored form, a2 –b2 = (a-b)(a+b)
Example:
36x2 – 25 = (6x)2 – (5)2
= (6x-5)(6x+5)