Review Multiply Polynomials and GCF

Multiply Polynomials
& Intro to Factoring

At the beginning of the year we learned how to multiply monomials by polynomials and binomials by each other.
To start the new unit, we will first review this!

9

Lesson Vocabulary

Image from mashupmath.com

Multiple Choice

Simplify this expression

$$x^2\cdot x$$  

• $$2x^2$$  

• $$x^3$$  

You can also use the area/box method that will be shown in a couple slide!

14

To multiply a polynomial by a

monomial, use Distributive Property.

MONOMIAL • POLYNOMIAL

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Multiple Select

Multiply: 5a²(7a³- 4a² + a - 2)

• 35a⁵ - 20a⁴ + 5a³ - 10a²

• 12a⁵ - 9a⁴ +5a³ - 7a²

• 35a⁶ -20a⁴ + 5a² - 10

Multiplying with variables

******Please get paper for next problems

Multiple Choice

Write the expanded (general) form of the product (x+3)(x+6).

• x²+18x+9

• x²+9x+18

• x²+18x+18

Multiple Choice

Find the product:
(y - 3)(y + 7)

• y² - 21
• y² + 10x - 21
• y² + 4y - 21
• 2y - 10

What's next?

In Unit 7 we'll focus on FACTORING polynomials. That's basically undoing the multiplication. This is an introduction!

What is Factoring?

• Separating a simplified polynomial back into a product.

• It is like "splitting" an expression into a multiplication of simpler expressions.

• Simplified Form 4a²+8a ---> Factored Form 4a(a+2)

• Polynomials that cannot be factored are called PRIME !

​GCF
Greatest Common Factor

What is the largest factor both values have in common?

Math Response

What is the GCF of 36 and 27.

Type answer here

Correct Answer: 9

Deg^°

Rad

Multiple Choice

What is the GCF of 15 and 20?

• 2

• 0

• 1

• 5

Multiple Choice

What is the GCF of 9 and 4?

• 0

• 1

• 3

• 5

Multiple Choice

What is the GCF of 56 and 80?

• 8

• 4

• 2

• 1

Multiple Choice

What is the GCF of 60 and 85?

• 1

• 7

• 12

• 5

Factor 8m+36n

• Both terms can be divided by 4

• 4(2m+9n)

• The terms left in the parentheses should NOT have any more common factors.

Multiple Choice

Factor 7y-7.

• 7(y-7)

• 1(7y-7)

• Prime

Factor 4y²-24y

• All terms can be divided by 4, and all terms contain at least 1 y.

• We factor OUT a 4y and the leftovers stay in the parentheses.

• 4y(y-6)

Factor 21cd+3d

• Both terms can be divided by 3 and they both contain at least 1 factor of d.

• We factor OUT a 3d and the leftovers stay in the parentheses.

• 3d(7c+1)

Factor 2x²y – 2xy²+ 4xy

• All terms can be divided by 2. They all contain at LEAST 1 x and 1 y

• They all contain at LEAST 1 x and 1 y

• So, we factor OUT a 2xy... and the leftovers go in parentheses.

• 2xy(x-y+2)

Factor 9r⁸ – 18r²s – 24rs²

• All terms can be divided by 3.

• All terms have at least 1 factor of r.

• Factor OUT 3r and leave the rest in parentheses.

• 3r(3r⁷-6rs-8s²)

​GCF
Greatest Common Factor

​What is the greatest common factor of each pairs of monomials?

​15y and 30y²

-5a²b² and -3ab

Open Ended

What is the greatest common factor of $$24x^4y^3-12x^2y+18xy^2$$