Factoring

FACTORING!!!!

By OLIVIA GREEN

​Springboard 26-1 Factoring GCF

26-1 Factoring - GCF

The greatest common factor (GCF) of the terms in a polynomial is the greatest monomial that divides into each term without a remainder!​

Not all polynomials can be factored.

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Find the GCF of....

15x⁴ and 3x²

20 and 64

-75x and -175​

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Objective: Identify the GCF and Factor the GCF from a polynomial​

Fill in the Blanks

What is the GCF of -18 and 72?

Fill in the Blanks

What is the GCF of the terms in the polynomial

36y - 24 ?

Factoring Polynomials

1) Identify the GCF of all monomials

2)Use distributive Property to Factor out the GCF​

Factor the polynomial

15t​²+10t-5

Your turn to Practice!!!

Fill in the Blanks

Rewrite 36y-24 by factoring out the GCF

Fill in the Blanks

Factor the polynomial:

36x+9

Fill in the Blanks

Factor the Polynomial:

6x⁴+12x²-18x

(Use the ^ symbol to express exponents example x^2 = x²)

Fill in the Blanks

Factor the polynomial:

125n⁶+250n⁵+25n³

Fill in the Blanks

Factor the polynomial:

3x³+9x²+6x

Fill in the Blanks

What is the GCF of the following polynomial:

$\frac{2}{3}y^4+\frac{1}{3}y^3-\frac{4}{3}y^2$  

(fractions can be written by writing the / sign)

Fill in the Blanks

What is the GCF of the following polynomial:

$4x^2y^2+12xy^2-8x^2y-4xy$  

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Homework:

26-1 in Math xl​

POP QUIZ OVER THIS MATERIAL COMING ;)

26-2 Factoring Special Cases

​PERFECT SQUARE TRINOMIALS​

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Objective: Factor a Perfect Square Trinomial & the Difference of Two Squares

Tri means fli

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• If you have a TRInomial then you should look at the First term and separate it, factor the Last term, and find the set that adds to be the Inner Term (FLI).

x²​+6x+9

x²​+9x+20

x²​+6x+8

Multiple Choice

What are the factors of the polynomial $$x^2+10x+25$$  ?

• $$\left(x+3\right)^2$$  

• $$\left(x+4\right)^2$$  

• $$\left(x+5\right)^2$$  

• $$\left(x-5\right)^2$$  

HINT:

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• NEGATIVE in the BACK that's so WHACK (+) (-) where the symbol in front goes to the largest factor.

• When the leading coefficient isn't prime you will have more possibilities for trial and error.​

• The larger number tends to get the first sign..

2x²​+7x+6 3x²​+8x-11 4x²​-4x-15

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6x²-13x-4​ Glance @ pg. 398 & 399

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Multiple Choice

Factor the trinomial $$6x^2-11x-2$$  

• $$\left(6x+1\right)\left(x-2\right)$$  

• $$\left(6x-2\right)\left(x+1\right)$$  

• $$\left(3x+1\right)\left(2x-2\right)$$  

• cannot be factored

Multiple Choice

Factor the trinomial

$$4x^2-20x+21$$  

• cannot be factored

• $$\left(2x-3\right)\left(2x-7\right)$$  

• (4x-3)(x-7)

• (2x-3)(2x+7)

Multiple Choice

Factor the trinomial

$$6x^2-13x-4$$  

• cannot be factored

• (6x+2)(x-1)

• (6x-2)(x+1)

• (3x-2)(2x+1)

Fill in the Blanks

Factor the trinomial

$5x^2+x-4$  

Multiple Choice

Factor the difference of two squares.

$$9-25p^2$$  

• (3+5p)(3+5p)

• (3+5p)(3-5p)

• (3-5p)(3-5p)

• cannot be factored

Fill in the Blanks

Factor the difference of two squares.

$x^2-121$  

Fill in the Blanks

Find the difference of two squares

$16m^2-81$  

Factor by Grouping

Objective: Factor by grouping.

4 terms = Group

-Sort it, group it, factor Completely

IXL Code: HAA

Review/ FACTOR ANYTHING!

• ​GCF

• Tri means fli

• ​difference of square is ( + ) (-)

• Grouping

• Calculator Factor Notes 2-2-8

YOU CAN USE MULTIPLY METHODS TO FACTOR!!!!

Example: 9x²-24x+12​

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Fill in the Blanks

Factor the trinomial completely.

$49x^2-126x+56$  

Fill in the Blanks

Factor the trinomial completely.

$8x^2+20x-28$  

That's it we've done it!!

You've learned how to factor, learned how to factor!!!

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Video Time ;)​​

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Homework:

IXL Starred Skills 27-1 & 27-2 for a grade!!!