POLYNOMIAL EQUATION

POLYNOMIAL EQUATION

by Edilmira Esturom

​RECALL

​FactorTheorem

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If P(a) = 0, then x – a is a factor of P(x).

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Conversely, if x – a is a factor of P(x), then P(a) = 0. 

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​ILLUSTRATES POLYNOMIAL EQUATION

Open Ended

What is the difference between an expression and an equation?

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What is the difference between an expression and an equation?

• ​ If a polynomial is an algebraic expression involving only nonnegativeinteger powers of one or more variable and containing no variable in the denominator.

• ​An algebraic equation is a mathematical statement stating that two algebraic expressions are equal.

​POLYNOMIAL EQUATION

​Degree of a polynomial equation

degree of the term with the highest degree in the polynomial.

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​POLYNOMIAL OR NOT?

Multiple Choice

$$x^3+12x^2-8x-10=0$$  

• POLYNOMIAL

• NOT POLYNOMIAL

Multiple Choice

$$ax^2+xy-3=0$$  

• POLYNOMIAL

• NOT POLYNOMIAL

Multiple Choice

$$2x^6+3x^{-2}=4$$  

• POLYNOMIAL

• NOT POLYNOMIAL

Multiple Choice

$$x^3+2x$$  

• POLYNOMIAL

• NOT POLYNOMIAL

Multiple Choice

$$5x-\frac{1}{x}=0$$  

• POLYNOMIAL

• NOT POLYNOMIAL

Multiple Choice

$$\frac{1}{2}x^2+x+20=0$$  

• POLYNOMIAL

• NOT POLYNOMIAL

Multiple Choice

$$3x-1=2x^2$$  

• POLYNOMIAL

• NOT POLYNOMIAL

Multiple Choice

$$6x^{\frac{2}{3}}=3$$  

• POLYNOMIAL

• NOT POLYNOMIAL

​WHAT΄S MY DEGREE?

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

​FINDING THE ROOTS OF A POLYNOMIAL EQUATION

​1. E

​2. C

​3. D

​4. A

​5. B

​RECALL

• ​SOLUTION a specific number when replaced to a variable and the result is true then that number is called a solution (or root) of the equation.​

• ​ SOLUTION SET is the set of all the solutions that satisfy the equation. ​ Examples: 1) −4 is a root of the equation x + 4= 0 because when −4 is substituted to x, it makes the equation true. 2). 2 is NOT a root of the equation x + 4=0 2 + 4 = 0 because when 2 is substituted to x, it makes the equation false.

THEOREMS IN POLYNOMIAL EQUATIONS

​PROCEDURES IN FINDING THE ROOTS OF POLYNOMIAL EQUATION

Open Ended

​Example 1:

Find the roots of  $$x^{3\ }+\ 2x^2-5x-6=0$$  

​ c.) (x + 1) (x + 3) (x - 2) = 0.

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​ 3.) (x + 1) (x + 3) (x - 2) = 0

a.) x +1 = 0

x + 3 = 0

x – 2 = 0

x = −1 x = −3 x = 2

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b) Therefore, the roots are: { −1, −3, 2}.

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Open Ended

Example 2. Find the roots of 2m⁴ + 3m³ – 7m² – 12m – 4 = 0.

​Example 2. Find the roots of 2m⁴ + 3m³ – 7m² – 12m – 4 = 0.

Open Ended

Example 3. Find the roots of k³ + 8k² + 18k +12 = 0.

​Example 3. Find the roots of k³ + 8k² + 18k +12 = 0.

​b) Therefore, the roots are: { -2, −𝟑 ± √𝟑 }.

​a.)

Open Ended

Example 4. Find the roots of b³ – 4b² + 7b – 4 = 0.

Example 4. Find the roots of b³ – 4b² + 7b – 4 = 0.

​a.)

​ Oops!

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​You Passed QUARTER 1!

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​See you in Quarter 2!

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​THANK YOU!