Illustrating and Simplifying Rational Algebraic Expressions

by Jinky Legaspi

Illustrating and Simplifying

Rational Algebraic Expressions

IDentify if the given expression is a polynomial or not.

Multiple Choice

$$x^2-\sqrt[]{y}$$  

• POLYNOMIAL

• NOT Polynomial

Multiple Choice

$$x^{-2}+y$$  

• POLYNOMIAL

• NOT Polynomial

Multiple Choice

$$\frac{2}{y}+3y$$  

• POLYNOMIAL

• NOT Polynomial

Multiple Choice

$$3y-2y^x$$  

• POLYNOMIAL

• NOT Polynomial

Multiple Choice

$$\frac{1}{3}x-2y^3+\sqrt[]{3}z+\frac{y}{3}$$  

• POLYNOMIAL

• NOT Polynomial

WHAT ARE THE DIFFERENT WAYS TO FACTOR A POLYNOMIAL?

Fill in the Blanks

Factorization of Polynomials with  DOTS pattern.

What is DOTS?

Fill in the Blanks

Factorization of Polynomials by factoring out the GCMF.

What is GCMF?

Fill in the Blanks

Factorization of PST.

What is PST?

Multiple Choice

Factorization of PST.

What pattern use for Factorization of PST?

Given:  $$a^2+2ab+b^2$$  

• (a-b)(a+b)

• (a-b)(a-b)

• (a+b)(a+b)

• (a+b)(a-b)

Multiple Choice

Factorization of PST.

What pattern use for Factorization of PST?

Given:  $$a^2-2ab+b^2$$  

• (a-b)(a+b)

• (a-b)(a-b)

• (a+b)(a+b)

• (a+b)(a-b)

​

​Watch Video for Factoring PST

Multiple Choice

Factorization with SDTC pattern.

What is SDTC?

• Sum and Difference of Two Circles

• Sum and Difference of Two Cubes

• Sum and Difference of Two Cutes

Multiple Choice

Factorization with SDTC pattern.

Which one shows the pattern in factoring SDTC

$$a^3-b^3$$  

• $$\left(a-b\right)\left(a^2+ab+b^2\right)$$  

• $$\left(a-b\right)\left(a^2-ab-b^2\right)$$

• $$\left(a-b\right)\left(a^2-ab+b^2\right)$$

​Illustrating

RATIONAL

ALGEBRAIC

EXPRESSION

​ANSWER:

​1. RAE

​2. NR

​3. NR

​4. RAE

​5. NR

Multiple Choice

RAE or NOT RAE?

$$2x^2+1$$  

• RAE

• NOT RAE

​Explanation:

​DOMAIN

​the domain of a rational algebraic expression includes all real numbers except for those that make its denominator zero.

TARGET: The denominator should not be zero.

​Example:

Multiple Choice

Identify the values that is NOT part of the DOMAIN $$\left(x\right)$$   of the given Rational Algebraic Expression,

$$\frac{x+1}{7+x}$$  

• $$x\ne-7$$  

• $$x\ne7$$  

• $$x\ne-1$$  

• $$x\ne\frac{1}{2}$$  

Multiple Choice

Identify the values that is NOT part of the DOMAIN $$\left(x\right)$$   of the given Rational Algebraic Expression,

$$\frac{3x-7}{2x+1}$$  

• $$x\ne-1$$  

• $$x\ne-\frac{1}{2}$$  

• $$x\ne1$$  

• $$x\ne\frac{1}{2}$$  

Multiple Choice

Identify the values that is NOT part of the DOMAIN $$\left(x\right)$$   of the given Rational Algebraic Expression,

$$\frac{x+1}{\left(x-3\right)\left(x+4\right)}$$  

• $$x\ne-3\ or\ x\ne-4$$  

• $$x\ne3\ or\ x\ne-4$$  

• $$x\ne-3\ or\ x\ne4$$  

• $$x\ne3\ or\ x\ne4$$  

Multiple Choice

Identify the values that is NOT part of the DOMAIN $$\left(x\right)$$   of the given Rational Algebraic Expression,

$$\frac{2x-3}{x\left(x+1\right)}$$  

• $$x\ne1$$  

• $$x\ne-1$$  

• $$x\ne0\ or\ x\ne1$$  

• $$x\ne0\ or\ x\ne-1$$  

​SIMPLIFYING

RATIONAL ALGEBRAIC EXPRESSION​

​SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSION

Multiple Choice

Simplify the given Rational Algebraic Expression,

$$-\frac{36x^3}{42x^2}$$  

• $$\frac{6x}{7}$$  

• $$-\frac{6x}{7}$$  

• $$\frac{6}{7x}$$  

• $$-\frac{6}{7x}$$  

​Solution:

Multiple Choice

Simplify the given Rational Algebraic Expression,

$$\frac{15n}{30n^3}$$  

• $$\frac{1}{2n^2}$$  

• $$\frac{1}{2n^{ }}$$  

• $$\frac{1n^2}{2}$$  

• $$\frac{1}{2}$$  

​Solution:

​SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSION

Multiple Choice

Simplify the given Rational Algebraic Expression,

$$\frac{b^2+3b-28}{b^2-49}$$  

• $$\frac{b-4}{b+7}$$  

• $$\frac{b+4}{b+7}$$  

• $$\frac{b-4}{b-7}$$  

• $$\frac{b+4}{b-7}$$  

​Solution:

Multiple Choice

Simplify the given Rational Algebraic Expression,

$$\frac{2n-2}{6n-20}$$  

• $$\frac{n-1}{3n-10}$$  

• $$\frac{2\left(n-1\right)}{6\left(n-10\right)}$$  

• $$\frac{2n-2}{3n-10}$$  

​Solution:

​SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSION

Multiple Choice

Simplify the given Rational Algebraic Expression,

$$\frac{n^2-9n+20}{n^2-6n+8}$$  

• $$\frac{n+5}{n-2}$$  

• $$\frac{n-5}{n+2}$$  

• $$\frac{n-5}{n-2}$$  

• $$\frac{n+5}{n+2}$$  

​