March 25, 2015

Today:Warm-Up:

Review Monday's Topics & Friday's TestContinue: Factoring (ax2 + bx + c) Trinomials Reminder: Khan Academy Due by Tonight, New

Topics MondayClass Work

25

Warm-Up: Test Review(8)

3. 9/49x² - 4

1. (1/2x - y)(1/2x + y) 2. x² - 1/16 2. (x - 1/4)(x + 1/4)

3. (3/7x+2)(3/7x- 2) 4. x2 + 8x - 48

7. x2 - 10xy + 25y2

1. 1/4x² - y²

4. (x + 12) (x - 4)

Factor or expand each expression completely:

5. (2x + 3y)² 5. (4x² + 12xy + 9y²) 6. (.25a – .36b)²

6. (.5a + .6b)(.5a - .6b)

Class Notes Section of your Notebook:

8. (x2 + 9y)² 8. (x4 + 18xy + y2 )

7. (x - 5y)2

Perfect Square Trinomial

1. PST's have a square in the first & third terms: The first & third terms are always positive.

2. The factors of PST's are always either the square of a sum (x + y)², or the square of a difference (x - y)²

3. To determine whether a trinomial is a PST, one of two tests need to be applied. They are:

The middle term is twice the product of

the square root of the first term and the

square root of the third term. or b 2

2must = A*C

Recognizing & Factoring Perfect Square Trinomials

Factoring 2nd degree trinomials

with a leading coefficient > 1

Factoring (ax2 + bx + c) Trinomials

Method #1: Grouping

Step

1Multiply the leading coefficient and the constant

term

Method #1: Grouping

25x2 + 20x + 4

25 • 4 = 100

Step 2Find the two factors of 100 that add to

the coefficient of the middle term.

Notice the 'plus, plus' signs in the

original trinomial.

Factors of 100:

1 100

2 50

4 25

5 20

10 10

Our two factors are10 &

10

25x2 + 20x + 4

Step 3Re-write the original trinomial

and replace 10x with 6x + 4x.

Step

4 Factor by Grouping

25x2 + 20x + 425x2 + 10x + 10x + 4

(25x2 + 10x) + (10x + 4)

Step

5 Factor out the GCF of each pair of

terms

After doing so, you will have...

Step

6 Factor out the common binomial.

(25x2 + 10x) + (10x + 4)

5x(5x + 2) + 2(5x + 2)

(5x + 2)(5x + 2)

Pair the remaining terms together.The final factorization is? A PST!(5x + 2)2

A 5 second check before solving saves time and possibly incorrect factoring.

Practice: Factor by GroupingFactor: 30x2 - 27x + 6In this case, step 1 is...

and we are left with.. 3(10x2 - 9x + 2)

1 20

2 10

4 5

Multiply the leading coefficient and the constant

termFactors of 20: Our two factors are 4 & 5Re-write the original trinomialand replace -9x with -4x & -5x. 3(10x2 - 5x - 4x +

2)Factor by Grouping 3(10x2 - 5x) -

?3 • 5x(2x - 1) - 2(2x - 1)

=

3(2x - 1)(5x -

2)

Factor

the GCF

The signs of the factors will be: ( - ) ( - )

(4x - 2) =

Method #2: The Box Method

Using the Box Method to factor (ax2 + bx + c)

Trinomials

9x3 + 12x2 + 4x

As usual, we

are looking

for factors

that add to

'b', and

multiply to

'ac'

Is there a GCF

to Factor?x(9x2 + 12x + 4)

3x,3x

9x, x

4,1:

2,2

3x 3x

1.Draw binomials with correct signs

4

1x( + )( +

)2. Multiply diagonally to mentally check, or fill in the binomial.

3x 4 3x 13x 2 3x 2

x( 3x+2)(3x +2)or,The correct factorization is:

x( 3x + 2)2

Factors

of 'a'

2

2

Practice: Factor using the Box Method10x2 + 21x -

10

10,-1: -

10,1

5,-2: -5,2

10x,x

5x,2x

Factors

of 'a'

Draw binomials with correct

signs( - )( +

)

( 2x+5)(5x- 2)

5x 2x

-5 2

That doesn't work, so we'll

try

-2 5

Method #3: Trial & Error

Task: Factor the polynomial (25x2 +101x + 4)

Possible factors of 25x2 are

Possible factors of 4 are

We need to try each pair of factors until we find a combination that works, or exhaust all of our possible pairs of factors.

Keep in mind that, because some of our pairs are not identical factors, we may have to switch some pairs of factors and make 2 attempts before we can definitely decide a particular pair of factors will not work.

Method #3: Trial & Error

{x, 25x} or {5x, 5x}.

{1, 4} or {2, 2}.

We are looking for a combination that gives the sums to the middle term and are factors of the last term

{5x, 5x} {2, 2} (5x + 2)(5x + 2)

Method #3: Trial & Error

{x, 25x} {2, 2} (x + 2)(25x + 2)

10x 10x 20x

4x 25x 29x

2x 50x 52x

x 100x 101x

(25x2 +101x + 4)

(x + 4)(25x + 1)

{x, 25x} {1, 4} (x + 1)(25x + 4)

Class Work: 3.10 & Study Guide

for Test

1. If you want to keep the handout for class work 3.10, write the questions on separate sheet of paper

2. Try to solve the questions on the study guide, as the test will look very similar.

On Class Work 3.10, Replace questions 11, 12, 13, 15 with3. x2 - 11x + 24 4. 32 - 8z2

5. 3a2 - 24ab + 48b2 6. v2q2 - .49r2