Question

mat151 college algebra dual-enrollment (25-26) > assessment
test review #3, chapter 5
score: 5/37 answered: 5/37
question 6
given ( f(x) = 6(x + 1)^4(x - 1)^3(5x - 3)^3(x - 2)^4 )
list the zeroes (ex. 4, 6, -2):
degree:
end behavior:
as ( x \to -infty ), ( f(x) \to ) +∞
as ( x \to +infty ), ( f(x) \to ) -∞
question help: video 1 video 2

Explanation:

Step1: Find zeros by setting factors to 0

Set each factor equal to 0:
$x+1=0 \implies x=-1$
$x-1=0 \implies x=1$
$5x-3=0 \implies x=\frac{3}{5}$
$x-2=0 \implies x=2$

Step2: Calculate degree of polynomial

Add exponents of all factors:
$4+3+3+4=14$

Step3: Determine end behavior

Leading coefficient is positive ($6>0$), degree is even (14). For even degree with positive leading coefficient:
As $x \to -\infty$, $f(x) \to +\infty$; As $x \to +\infty$, $f(x) \to +\infty$

Answer:

Zeros: $-1, 1, \frac{3}{5}, 2$
Degree: $14$
End behavior:
As $x \to -\infty$, $f(x) \to +\infty$
As $x \to +\infty$, $f(x) \to +\infty$