Learning Task 1. Identify if the given equation is a polynomial equation or not.
Write P if polynomial equation and NP if not.
1.3x4 + 5x - 3 = 0
2.2x4 + 2x3 - 6x +12 = 0
3.x3 - 6x-2- - X - 1 = 0
4.x5 - 32 = 0
5.x2 -
= 0
6.x2 +
- 2 = 0
= 0
17.5x3 + 4x9 - X3 +
4
8. x3 x + 3 = 0
V3
9. (x - 3) (x2 4x) = 0
2
10. x (x - 2)(3x + 5) = 0
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Polynomial Equation
Equation formed with variables, exponents, and coefficients together with operations and an equal sign. Polynomial Equations - the relation between numbers and variables are explained in a pattern. Polynomial Equations are also form an algebraic equations.polynomial equation is expressed in the form of a_n(xⁿ). a is the coefficient, x is the variable, n is the exponent.
Answers:
Solutions:
1. 3x⁴ + 5x - 3 = 0
This is a polynomial equation since all the exponents in the equation are non - negative integers and there is no radical in it.
2. 2x⁴ + 2x³ - 6x + 12 = 0
This is a polynomial equation since all the exponents in the equation are non - negative integers and there is no radical in it.
3. x³ - 6x⁻² - X - 1 = 0
This is not a polynomial equation because of the negative exponent in the second term.
4. x⁵ - 32 = 0
This is a polynomial equation since all the exponents in the equation are non - negative integers and there is no radical in it.
5. x² - [tex]\frac{1}{4}[/tex] = 0
This is a polynomial equation since all the exponents in the equation are non - negative integers and there is no radical in it.
6. x² + [tex]\sqrt{x}[/tex] - 2 = 0
This is not a polynomial equation because of the radical.
7. 5x³ + 4x⁹ - x³ + [tex]\sqrt{3}[/tex] = 0
This is not a polynomial equation because of the radical.
8. x³ - [tex]\frac{2}{x}[/tex] + 3 = 0
This is a polynomial equation since all the exponents in the equation are non - negative integers and there is no radical in it.
9. (x - 3) (x² - 4x) = 0
This is a polynomial equation since all the exponents in the equation are non - negative integers and there is no radical in it.
10. x (x - 2)(3x + 5) = 0
This is a polynomial equation since all the exponents in the equation are non - negative integers and there is no radical in it.
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