Polynomial Functions and solving Polynomial Equations
The Remainder and Factor Theorems
Roots and Zeros
100
This exponent property says that you keep the base and add the exponent.
What is the Product of Powers?
100
Is a simpler process for dividing a polynomial by a binomial.
What is synthetic division?
100
Classify by degree and number of terms: 4x-2
What is a linear binomial?
100
if f(x)=3x^4 - 2x^3 + 5x + 2, find f(4).
f(4)=662
100
Solve: x^3 + 25x =0.
What is x=0; x= +5i or -5i.
200
This exponent property says that you keep the base and subtract the exponents.
What is the Quotient of Powers?
200
Divide: (x^2+3x-40)/(x-5)
What is x+8
200
Classify by degree and number of terms: 3x^3 -10x+ 9x^5- 2
What is a quintic polynomial?
200
A factor of x^3 - 7x^2 +7x + 15 is x-5. Find the remaining factors.
What are (x-3) and (x+1)?
200
Solve: x^2+6x+9=0
What is x= -3?
300
This exponent property says that you keep the base and multiply the exponents.
What is the Power of a power?
300
Use synthetic division to find the quotient: (2x^3-13x^2+26x-24) /(x-4)
What is 2x^2-5x+6
300
Find the f(3c-4) - 5f(c) if f(x)= x^2 +2x-3.
4c^2-28c+20
300
If f(x)=3x^4 - 2x^3 +5x +2, then find the f(2).
What is 44?
300
This theorem says that for any polynomial function with real coefficients, if an imaginary number is a zero of that function, its conjugate is also a zero.
What is the Complex Conjugates Theorem?
400
Simplify: (4x^2-5x+6) - (2x^2 +3x -1)
What is 2x^2-8x=7?
400
(a^2+7a-11)(3-a)^-1
What is -a-10+(19/3-a)
400
Is the domain and range of an odd degree function, with a positive coefficient.
What is all real Numbers?
400
Find the f(2), if f(x)=3x^2 -9
What is 3?
400
Write a polynomial function of least degree with integral coefficients, the zeros of which include -1 and 5-i.
What is x^3 - 9x^2 +16x + 26?
500
Is a number, a variable, or an expression that is the product of one or more variables with nonnegative exponents.
What is a monomial?
500
The process of dividing a polynomial by a polynomial with more than one term.
What is the division algorithm?
500
Is the end behavior of an even degree, positive leading coefficient function.
What is: f(x) approaches positive infinity as x approaches negative infinity, and f(x) approaches positive infinity and as x approaches positive infinity?