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?

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,

$$\frac{n^2-9n+20}{n^2-6n+8}$$  

• $$\frac{n+5}{n-2}$$  

• $$\frac{n-5}{n+2}$$  

• $$\frac{n-5}{n-2}$$  

• $$\frac{n+5}{n+2}$$  

​