Classifying Polynomials
Write the polynomial in standard form: -7 - 3x3+ 4x5 +2x2
4x5 - 3x3 + 2x2 -7
Find the zeros of the function: y = (x - 3)(x + 2)
-2, 3
Which special points on graphs will help you to find its zeros?
The X-intercepts
When do you have an imaginary zero?
when the discriminant equals a negative number
(-6x2)(5x)
-30x3
Classify the polynomial by the number of terms (provide the name): x3 + 2
Binomial
What does zero's of a function mean?
Zero's mean that the x-values make the expression =0
Sketch a graph of a polynomial that has two zeros.
a parabola whose vertex is below the x axis
How many imaginary zero's can a cubic equation have?
2
What is the fundamental theorem of algebra? Give an example and explain. Write it down
The degree of a polynomial determine the number of solutions
Classify the polynomial by degree (provide the name): 5x3 - 3x + 12
Cubic
Find the zeros of the function: y = x(x + 1)(x - 7)
-1, 0, 7
Draw a polynomial graph that has no real zeros.
Dr. Favors will determine.
True or False: A cubic polynomial has no real zeros. Must explain answer
False
(-3a2 - 2a) - (4a2 - 4)
-7a2 - 2a + 4
Classify the polynomial by degree and number of terms (provide the names): -2x4
Quartic monomial
Write a polynomial function in standard form with the given zeros: 5, 4
x2 - 9x + 20
Sketch a graph of a polynomial that has five zeros.
Dr. Favors will determine.
True or False. A quartic polynomial has 2 or 4 imaginary zeros. Must explain the answer.
True
(4 - x - 2x2) - (-2 + 3x - x3)
x3 - 2x2 - 4x + 6
Write in standard form, then classify the polynomial by degree and number of terms (provide the names): 3x3 + 8 - x3 - 7x2
2x3 - 7x2 + 8; cubic trinomial
Write a polynomial function in standard form with the given zeros: 1, -1, -2
x3 + 2x2 - x - 2
Explain why finding a zero is the same as finding an x-intercept
Because the x-intercept is the value of x that makes the expression = 0
Find all possible real and imaginary roots of a degree 6 polynomial
Real:imaginary 0:6, 2:4, 4:2, 6:0
Find the discriminant and state the number and type of solutions. 12x + 9 = -4x2
Discriminant = 0 , One Real Solution