y=3+12x^4
y=-3x+6x^2-1
y=5-x^2-x^3
Can someone help me with these problems? I need to know how to find the classification and i dont understand it.
Classification?
I know that
Polynomials of the first degree are called linear polynomials.
Infact
Polynomials of the nth degree are called nth degree polynomials.
We have
Monomial (highest degree is 1)
Binomial (......2)
Trinomial (.......3)
Polynomial (.....4)
Kenny, what you describe as monomial, binomial, trinomial and quadrinomial
refers to the number of terms in an expression.
What you want here is a classification based on the highest power.
so ...
y=3+12x^4 <----- Quartic polynomial, the highest power is a 4th degree
y=-3x+6x^2-1<----- quadratic
y=5-x^2-x^3 <----- cubic
y = 2x + 5 would be linear.
Okay sir ..... thought the information would help him/her BTW....but thank you...
It did help! Thank you both
To classify these equations, you need to determine their degree and type. The degree of an equation is the highest power of the variable present in the equation.
Let's analyze each equation step by step and determine their classification:
1. y = 3 + 12x^4
This equation is a polynomial equation, and its highest power of x is 4. Therefore, the degree of this equation is 4. Since the degree is even and the leading coefficient (the coefficient of the highest power term) is positive, this equation is classified as a quartic polynomial.
2. y = -3x + 6x^2 - 1
Like the previous equation, this is also a polynomial equation. The highest power of x is 2, so the degree of this equation is 2. Since the degree is even and the leading coefficient (the coefficient of the highest power term) is positive, this equation is classified as a quadratic polynomial.
3. y = 5 - x^2 - x^3
Again, this is a polynomial equation. The highest power of x is 3, so the degree is 3. Since the degree is odd and there is no leading coefficient specified, it is assumed to be positive. Therefore, this equation is classified as a cubic polynomial.
To classify a polynomial equation, you need to look at the degree (even or odd) and the sign of the leading coefficient. Other types of equations include linear equations (degree 1), quadratic equations (degree 2), cubic equations (degree 3), and so on.