Factor or No Factor
When using synthetic division, how would we know if (x-3) is a factor of a polynomial?
What is the remainder is zero?
If a polynomial has an odd degree do the ends go in the same or opposite directions?
What is opposite directions?
Is x= -2 a zero of x2+5x+6?
What is, yes!
(x+2) is a factor making x=-2 a zero.
If a root has an odd multiplicity, will the graph of the function cross the x-axis?
What is yes?
What is Mr. Vazquez's favorite color?
What is Blue?
Is (x+2) a factor of x2+5x+6?
What is Yes?
x2+5x+6 = (x+2)(x+3)
If f(x) is an even function with positive leading coefficient, what is the end behavior of the graph of f(x)?
What is?
As x goes to the left, f(x) goes to infinity,
and
As x goes to the right, f(x) goes to infinity?
Why wouldn't a root of a polynomial also be an x-intercept?
What is it's an imaginary root?
What is the multiplicity of the the root x=2 in the polynomial f(x) = (x-3)3(x-1)2(x-2)4
What is multiplicity of x=2 is 4?
Does Mr. Vazquez prefer coffee or tea?
What is coffee?
If x= 3 and x=-5 are zeroes of f(x), what are two factors of f(x)?
What are (x-3) and (x+5)?
Given that g(x)= 2x5-3x2+6x-18, what is the will be the end behavior of g(x)?
What is:
As x goes to the left, g(x) goes negative infinity
and
As x goes to the right, g(x) goes to infinity?
How many x-intercepts will f(x) = x3-3x2+4x-12 have if x=3 is a root?
What is 1 x-intercept?
Given that k(x) = 2(x-3)(x+2)2(x-5), what will the graph of k(x) do at x=-2?
What is it will bounce?
Name two of Mr. Vazquez's Top 4 favorite movies.
What is
Good Will Hunting,
Ratatoullie,
Cars,
When Harry Met Sally?
Completely factor x5-4x4+3x3-12x2-4x+16 given that it has roots of x=1 and x=-1
What is
f(x) = (x-1)(x+1)(x+2i)(x-2i)(x-4)
?
Given that f(x) = -0.5(x-3)(x-2)(x-1)2(x+4)3, what will be the end behavior of f(x)?
What is:
As x goes to the left, f(x) goes to infinity,
and
As x goes to the right, f(x) goes to negative infinity?
Name all the roots of k(x) = f(x) = x⁵ + 3x⁴ − 15x³ − 7x² + 4x + 60? (Hint: (x-1) is a factor)
What is x=1 (2), -2,3,-5?
DAILY DOUBLE!!!
Sketch the graph of
f(x) = 2(x+1)(x-1)2(x-2)2(x-3)2(x-4)
What is Mr. Vazquez will check your drawing?
What is the name of Mr. Vazquez's cat and dog?
Who is Benji and Gumby?