Polynomials Flashcards
What is the degree of a polynomial?
The highest power in a polynomial.
What is the leading coefficient of a polynomial?
The number out the front of the highest power.
What is a monic polynomial?
A polynomial with a leading coefficient of 1.
What is the constant term of a polynomial?
The term unrelated to x.
How do you divide a polynomial?
- See how many times the degree goes into the first term.
- Add this number above the term being divided.
- Multiply this same number by the whole polynomial you’re dividing by.
- Subtract these terms from the polynomial being divided.
- Any left over terms are added to the end.
How do you find if a number is a root of a polynomial?
Substitute the number into P(x), and if P(x) = 0, the number is a root.
What characteristics of a polynomial are used when sketching polynomials?
The degree determines the basic shape.
The sign of the leading coefficient determines the direction.
The roots determine the x-intercepts.
The constant term determines the y-intercept.
When will different polynomials have the same roots?
When they entire equation is multiplied by a number.
In a quadratic equation, what does a + B equal?
a
In a quadratic equation, what does aB equal?
a
What does alpha x beta x gamma x delta equal?
a
What do all of the possible combinations of the roots of a polynomial examined three at a time equal?
a
What does alpha^2 + beta^2 equal?
(alpha + beta)^2 - 2(alpha beta)
What is a cardinal number?
A whole and positive number.
