MATH 8-QUARTER 1 WEEK 1(Factoring Polynomials)

​MATHEMATICS 8

QUARTER 1

WEEK 1​

​Quarter 1, Week 1

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At the end of the session, I would be able to:

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1. M8ALIa-b-1: Factor completely different types of polynomials (polynomials with common monomial factor, difference of two squares, sum and difference of two cubes, perfect square trinomials, and general trinomials).

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2. M8AL-Ib-2: Solve problems involving factors of polynomials.

FACTORING POLYNOMIALS

​What is the meaning of factoring polynomials?

​Definitions:

Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying.

To factor polynomials, we generally make use of the following properties or identities; along with other techniques.

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​Factoring:

• Common Monomial Factor

• Difference of Two Squares

• Sum or Difference of Two Cubes

• ​Perfect Square Trinomial

• ​Quadratic Trinomials

​Factoring:

• Common Monomial Factor

​Factoring:

• Difference of Two Squares

​Factoring:

• Sum of Two Cubes

​Factoring:

• Difference of Two Cubes

​Factoring:

• Perfect Square Trinomial

​Factoring:

• Quadratic Trinomials

​Factoring:

• Quadratic Trinomials

​Factoring:

• Common Monomial Factor

• Difference of Two Squares

• Sum or Difference of Two Cubes

• ​Perfect Square Trinomial

• ​Quadratic Trinomials

Multiple Choice

What factoring I will use in this polynomial?

5x + 15y

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

5x + 15y

• 5x(1+3y)

• 5y(x+3)

• 5(x+3y)

• 5(1+3y)

Multiple Choice

What factoring I will use in this polynomial?

$$9a^2-30a+25$$  

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

$$9a^2-30a+25$$  

• $$\left(3a+5\right)^2$$  

• $$\left(3a-5\right)^2$$  

• $$\left(5a+3\right)^2$$  

• $$\left(5a-3\right)^2$$  

Multiple Choice

What factoring I will use in this polynomial?

$$1-729n^3$$  

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

$$1-729n^3$$  

• $$\left(1-9n\right)\left(1+9n+81n^2\right)$$  

• $$\left(1+9n\right)\left(1-9n+81n^2\right)$$  

• $$\left(1-9n\right)\left(1+9n-81n^2\right)$$  

• $$\left(1-9n\right)\left(1-9n+81n^2\right)$$  

Multiple Choice

What factoring I will use in this polynomial?

$$7x^2y+xy^3$$  

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

$$7x^2y+xy^3$$  

• $$xy\left(7x+y^2\right)$$  

• $$xy\left(7+y^2\right)$$  

• $$xy\left(7x+y^{ }\right)$$  

• $$xy\left(7+y^{ }\right)$$  

Multiple Choice

What factoring I will use in this polynomial?

$$49x^2-64a^2$$  

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

$$49x^2-64a^2$$  

• (7x-16a)(7x+16a)

• (7x-8a)(7x+8a)

• (7x-16a)(7x-16a)

• (7x-8a)(7x-8a)

Multiple Choice

What factoring I will use in this polynomial?

$$x^2+10x-24$$  

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

$$x^2+10x-24$$  

• (x-2)(x+12)

• (x+2)(x-12)

• (x-6)(x+4)

• (x-4)(x+6)

Multiple Choice

What factoring I will use in this polynomial?

$$a^4+ab^3$$  

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

$$a^4+ab^3$$  

• $$a\left(a^3+b^3\right)$$  

• $$a\left(a^{ }+b^3\right)$$  

• $$a\left(a^3+b^{ }\right)$$  

• $$a\left(a^{ }+b^{ }\right)$$  

Multiple Choice

What factoring I will use in this polynomial?

$$3x^2-11x+6$$  

• COMMON MONOMIAL FACTOR

• DIFFERENCE OF THE TWO SQUARES

• SUM OR DIFFERENCE OF TWO CUBES

• PERFECT SQUARE TRINOMIAL

• QUADRATIC TRINOMIAL

Multiple Choice

What is the correct factor of the given polynomial?

$$3x^2-11x+6$$  

• (3x - 2)(x - 3)

• (3x + 2)(x - 3)

• (3x - 2)(x + 3)

• (3x + 2)(x + 3)