Long Division
This is how you perform polynomial long division.
What is the same way you perform long division with constants, by repeatedly asking "how many times does my divisor go into my dividend"?
This is the remainder of x2+3x-5 divided by (x-1).
This is the theory that states that the factors of a polynomial's constant term over the factors of its leading coefficient can help find its solutions solutions.
What is the rational zeroes theorem?
This is a p/q list.
What is all factors of the constant term over all factors of the leading coefficient?
This is the number of roots a given polynomial has, counting repeated roots.
What is the polynomial's degree?
This is how you perform synthetic division.
What is given a binomial factor, you pull down the leading coefficient and multiply, then add, finally reducing the power of each term by one?
These are the possible rational roots of 6x6+x3-2.
What are positive and negative 1, 2, 1/2, 1/3, 2/3, and 1/6?
This is why polynomial division is useful/important.
What is to factor into binomial factors?
This is why long division differs from synthetic division.
What is long division is more time-consuming BUT can be used to divide with divisor polynomials larger than binomials?
This is x2+6x+8 divided by (x+2).
What is (x+4)?
This is how to determine the possible rational roots of a polynomial.
What is list all factors of the constant term over all factors of the leading coefficient (a p/q list)?
This is the degree of the polynomial resulting from polynomial division.
What is the numerator's degree minus the denominator's degree?
These are the possible rational roots of f(x) = 5x4-46x3+84x2-50x+7.
What is ±1, 7, 1/5, and 7/5?
This is the definition of a polynomial.
What is an expression involving addition or subtraction of positive-power terms only?
**DAILY DOUBLE**
It would be best to use this division strategy when solving a problem involving a binomial divisor.
What is synthetic division?
These are the two types of roots not discoverable by the rational zeroes theorem.
What are irrational and imaginary roots?
This is the remainder theorem.
What is a principle that states that the remainder of synthetic division will equal f(d), where d is the divisor of the division?
This is 2x4-30x2+20x+48 divided by x2-x-2.
What is 2(x2+x-12)?
This is the remainder theorem of synthetic division.
What is the remainder of synthetic division with a given divisor is the solution of that polynomial with that divisor as its input?
These are the possible rational roots of t6-64.
What are positive and negative 1, 2, 4, 8, 16, 32, and 64?
This is how the rational zeroes theorem can be used to solve a polynomial.
What is by making a p/q list of possible rational zeroes, testing those zeroes using division, simplifying into binomial factors, and solving those factors?