Post on 01-Oct-2020
transcript
10-4 Factoring Special Products
Homework Any Questions?
Factoring is the reverse process of multiplying polynomials.
You will be given a polynomial and you must figure out what 2 binomials would be multiplied together to equal it.
Today we are dealing with special cases only…
The three special cases are as follows:
a2 – b2 = (a + b)(a – b)
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
When you factor, you are writing the product that would equal the polynomial… just like jeopardy, they give you the answer and you figure out the question.
Stand UP! When I say go…
Perform 15 dips off the side of your desk.
4
Example 1: Factoring out a Monomial (one term)
Polynomial Common Factor Factored Form
3x + 6 3 3(x + 2)
5x2 – 15x 5x 5x(x – 3)
4x2 + 6x + 8 2 2(2x2 + 3x + 4)
Example 2: Binomial Square Patterns
To recognize the difference of two squares, look for coefficients that are squares and for variables that are raised to the second power
a2 – b2 = ?
(a + b)(a – b)
Factor the following:
A. 4x2 – 25 = ?
B. 25 – 49x2 = ? Think Square Root…
Answers: A. (2x + 5)(2x – 5) B. (5 + 7x)(5 – 7x)
To recognize a perfect square trinomial, remember that the first and last terms must be positive and perfect squares, and , and the middle term must be twice the product of a and b.
Example 3: Trinomial Patterns a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
Factor the following using trinomial patterns:
A. x2 – 4x + 4 = ?
B. 16y2 + 24y + 9 = ?
Again think square roots…
2a 2b
• Sometimes before you factor, you need to
remove a monomial then begin to factor.
Always do this step first so you never
forget!
Example 4: Removing a monomial
3 – 27 =
3( – 9) =
3(x + 3)(x – 3)
2x2x
Example 5: Factor the following: 64 – (x + 2)2
8 – (x + 2) 8 + (x + 2)
Distribute the signs 8 – x – 2 8 + x + 2
(6 – x) (10 + x)
Cool Photo of the Day
10
New Invention
Cool Photo of the Day
11 New Invention
Cool Photo of the Day
12 New Invention
Cool Photo of the Day
13 New Invention
Practice Factor out the greatest common monomial factor
Practice Factor the expression
Practice Factor the expression
Practice Factor the expression
1.
2.
3.
4.
Practice
Factor the expression
1.
2.
3.
Practice
Factor the expression
1.
2.
3.
Practice
Factor the expression
1.
2.
3.
Practice
Factor the expression
1.
2.
3.
Homework:
Pg 531 #5-27odds