Today:1. Warm-Up

2. New Khan Academy Topics3. Factoring Polynomials

4. Special Products5. Class Work

3/18/15

1. 5(4x - 4) - 3 = 372

4. A 20% profit was made on an item selling for $60. What was the cost of the item?

2. FACTOR: 3xy - 21y + 5x – 35

3. FACTOR: 6mx – 4m + 3rx – 2r

Warm-Up:

Linear vs. Quadratic Equations1. Write a Linear Equation, any linear equation2. Write the Linear Equation in both standard and slope-intercept form.

Fill in the blank: (In your notebook)

3. The highest degree of any linear equation is _______. The angle of the line depends on the _______, and every linear equation results in a ________ line.

1

slope

straight

4. Write the equation of the given line

Warm-Up:

Khan Academy Topics for this week:

Thursday: Factoring Quadratics 2

Class Notes Section of Notebook, please

PolynomialsFactoring

Today:1. Review

2. Factor x2 + bx + c Trinomials3. Special ProductsClass Notes Section of Notebook

Instead of simply memorizing rules & formulas, it really2 helps to understand why (for what purpose), you are adding, subtracting, factoring, etc.

Remember, terms are separated by + or – signs. (The terms are

all being added or subtracted). An example is: 10x2 + 15x

Factoring is finding an equal expression that is a product, that

is, the factors are multiplied. How do we factor 10x2 + 15x ???

The first step is to always look for a common factor. Is there one

for this polynomial? We factor out the GCF of 5x. What remains

is (2x + 3). The full factor is 5x(2x + 3).

10x2 + 15x = 5x(2x + 3)

We multiply factors to find the terms of a polynomial.

(These terms are either being added or subtracted.)

The Main Idea

Steps to Factoring Completely:1. Look for the GCF

2. Look for special cases.

a. difference of two squares,

b. perfect square trinomial

3. If a trinomial is not a perfect square, look for two different binomial factors.

coming soon..

4. If a polynomial has 4 terms, you can try to factor by grouping.

6. Not all polynomials can be factored.

...today

5. Understand what you are working with before you attempt to factor.

...yesterday

To solve these, we use FOIL in reverse.

x2 + x – 6 = (x ) ( x )

Check the signs:

Then, list all the factors of the last term, looking for the sum of the middle term, and the product of the last term.

Factoring Trinomials: (1x2 + bx + c)(The leading coefficient is always 1)

x2 + x – 6 =

x2 + x – 6 =6

1,6

2,3

(x + )(x - )

(x + 3)(x - 2 )

No algebra magic or wizardry here.

Factor and check for the correct fit.

When trinomials have a degree of “2”, they are known as quadratics.

FOIL With a Positive and a Negative

(x + 3)(x - 5)

F = (x•x) = x2

O = (x•-5) -5x

I = (3•x) +3x

L = (3•-5) -15

Answer: x2 - 2x - 15

The larger number is negative, so the middle term is negative.

(x - 3)(x + 5)

FOIL With a Negative and a Positive

The opposite of our first example. The larger number is positive, resulting in a

positive middle term.Answer: x2 + 2x - 15

...But I thought if the signs were different, the middle term was cancelled out?

This is true, but only if the two numbers are the same!

(3x + 5)(3x – 5)

Factor the polynomial x2 + 13x + 30. That was too easy, one more

Factor the polynomial x2 – 2x – 35.

Since our two numbers must have a product of – 35 and a sum of – 2, the two numbers will have to have different signs.

Factors of – 35 Sum of Factors

– 1, 35 34

1, – 35 – 34

– 5, 7 2

5, – 7 – 2

Factor: 2ab2 – 26ab – 60a

Square of a sum

Square of a difference

Difference of Squares

Special Products

**Be able to recognize them in both factored and expanded form

Products...Special9x2 - 16x2

Factor:

18y3 – 8y

4m2 – 49n2 =

(2m)2 – (7n)2 Difference of

squares

(2m + 7n)(2m – 7m)

What type of special

product are these? difference of squares:

Find each Product (Expand), or Factor:

Class Work 3.9 Ample class time was left for you to work on 3.9 as there are more than the average number of problems to complete

Friday is the absolute latest this class work will be accepted for credit.

Some problems will require more than one factoring

As mentioned earlier, be aware of difference of squares and the other two special products.