Multiply and Factor Polynomials

​Multiplication of Polynomials and Factoring

​Multiplication of Polynomial

Multiplication of Polynomials is highly anchored to the following competencies:

a. Law of exponents (specifically: Product law and Power law)

b. Understanding of Distributive Property of Multiplication​

Some text here about the topic of discussion

Multiple Choice

Which of the following will complete the sentence below:

"To find the product of two numbers with the same base, _____ the base and ______ the exponents.

• add & add

• multiply & add

• copy & copy

• copy & add

Multiple Choice

Which of the following is equal to a ( b + c )?

• a + b + c

• ab + ac

• ab + bc

• abc

When multiplying monomial to polynomial:

​

a. Distribute the monomial factor to every term of polynomial factor.

​

​b. Combine similar terms if necessary.

​

Study the given example. ​

Multiplication of monomial by polynomial.

Multiple Choice

$$5x\ \left(3x^2+2\right)$$  

• $$15x^3+10x$$  

• $$15x^2+10$$  

• $$15\ +\ 10x$$  

• $$8x\ ^3+\ 7x$$  

Multiple Choice

$$-3x\ \left(x^2-x\ +\ 11\right)$$  

• $$-3x^2+3x-33$$  

• $$-3x^4+3x^2+33x$$  

• $$-3x^4+3x^2-33x$$  

• $$-3+3x^2-11x$$  

Multiple Choice

$$3xy\left(2x^2+2xy+y^2\right)$$  

• $$5x^3y+5x^2y^2+3yxy^3$$  

• $$6x^3y+6x^2y^2+3xy^3$$  

• $$6x^2y+6xy+3xy^3$$  

• $$6x^3y+6x^2y^2+xy^3$$  

Replace this with your body text.

​Duplicate this text as many times as you would like.

​

​Some text here about the topic of discussion.

MULTIPLICATION OF BIN

There are several methods in performing multiplication of two binomials:

Method 1:

Using Distributive Property of Multiplication

​

Method 2:

Using FOIL Method

​

​

Please study the given examples.​

Multiplication of binomial to binomial

Method 1: Using Distributive Property of Multiplication

Method 2: Using FOIL Method

Multiple Choice

• $$36x^2-58x+24$$  

• $$36x^2-50x+24$$  

• $$9x-58+24$$  

• $$9x^2-58x+24$$  

Multiple Choice

• $$6x^2-57x+117$$  

• $$6x^2-21x+117$$  

• $$5x+57x+117$$  

• $$6x^2+57x+117$$  

Multiple Choice

• $$x^2-17+42$$  

• $$x^2-11x+42$$  

• $$x^2-17x+42$$  

• $$2x^2-17x+42$$  

Special products are the opposite process of factoring techniques.

​

​

Factoring Techniques and Special Products

Directions

Identify the factoring technique/special product that can be observed in the given example. Factor if the given is an expression, otherwise multiply.

​

Example: "Sum and Difference of Two Terms - Answer"​

Open Ended

$$m^3-36$$  

Open Ended

$$\left(2x\ +\ 3\right)^2$$  

Open Ended

$$m^2-4m+4$$  

Open Ended

$$3\left(x+4\right)\left(x-4\right)$$  

Open Ended

$$3\left(x+4\right)\left(x-4\right)$$  

Open Ended

$$\left(b+3c\right)\left(b^3-3bc+27c^3\right)$$  

​END

Thank you for taking the course