If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
Step-by-step explanation:
x = number of visits
y = number of earned points
the equation for the situation is (remember the 20 points starting balance) :
y = 5.5 × x + 20
and the question is now actually after how many visits she reached 75 earned points.
therefore,
75 = 5.5 × x + 20
55 = 5.5 × x
x = 55/5.5 = 10
she gets a free movie ticket after 10 visits.
Answer:
6ft
Step-by-step explanation:
first you need to properly provide your work
Answer:
the one the has the points of (4,5) and (-1,1)
Step-by-step explanation:
Answer:
14 & 6
Step-by-step explanation:
56/4=14
24/4=6