5.2 Polynomial Division and Division Algorithm
Use long division to rewrite
frac{2x^3+7x^2-5x+8}{x+2}
in the form
q(x)+\frac{r(x)}{d(x)}
2x^2+3x-11+(30)/(x+2_
Construct a quadratic polynomial with zeros −4,3 that goes to +∞ as x→∞.
f(x)=x^2+x-12
Find the degree and the y-intercept of
f(x)=(x-2)^3(x+1)^2
Express the y-intercept as an ordered pair.
y-intercept=(0,-8)
Find the equation of the vertical asymptote, if any.
f(x)=(8x^2+10x-3)/(2x-1)
Factor the numerator:
8x^2+10x-3=(4x-1)(2x+3)
Factor the denominator 2x-1=0
x=1/2
Solve
8^x=64
x=2
Find the amount after 4 years is $4,000 is invested at 5% compounded yearly.
$4,862.03
Use synthetic division to determine whether
k=−2 is a zero of
p(x)=x^3-4x^2-7x+10
If not, determine p(−2).
yes, p(-2)=0
Use the Rational Zero Theorem to list all possible rational zeros of
f(x)=x^3-7x^2-8x+56
±1,±2,±4,±7,±8,±14,±28,±56
Consider
f(x)=(x+4)^2(x-1)^3
Find every x-intercept where the graph crosses the x-axis.
(1,0)
Find the equation of the vertical and Horizontal asymptote.
f(x)=(5x+4)/(x+6)
Vertical: x=-6
Horizontal: y=5
Solve
9^(2x)=81
2X=2
X=1
A savings account contains $6,000. Earning 4% annual interest compounded monthly, how much will be in the account after 3 years?
$6,767.59
Use polynomial long division to rewrite
frac{4x^3-5x^2+9x-6}{2x-1}
in the form
q(x)+\frac{r(x)}{d(x)}
2x^2-(3)/(2)x+15/4-9/4(2x-1)
or
2x^2-(3)/(2)x+15/4+(-9/4)/(2x-1)
Find all real zeros.
f(x)=x^3-9x^2+14x+24
x=-1, 4, 6
Consider
f(x)=(x-2)^4(x+5)
Find every zero where the graph flattens out.
(2,0)
Find the equation of the vertical and horizontal asymptote.
f(x)= (3x-7)/(2x+5)
Vertical: x=-5/2
Horizontal: y=3/2
Solve
25^(x-1)=5^4
2(x-1)=4
2x=6
x=3
the population of a town is modeled by P(t)=120000e^(0.03t) find the population after 8 years.
152,570 people
Use synthetic division to determine p(3) if
p(x)=3x^4-8x^3+5x^2-9x+4
p(3)=49
Find all solutions.
x^3-6x^2-7x+60=0
x=-3, 4,5
Find all zeros of
f(x)=x^3-5x^2-2x+24
(Be sure to find the appropriate number of solutions.)
x=-2, 3, 4
Solve the rational inequality
(x-2)/(x+3)≥0
(−∞,−3)∪[2,∞)
x= -3, 2
Solve
16^x=32
(2^4)^x=2^5
4x=5
x=5/4
a city has 500000 people and is declining according to
P(t)-500000e^(-0.015t) find the population after 10 years.
430,354 people
Use polynomial long division to rewrite
frac{5x^4-2x^3+7x^2+6x-9}{x^2+2}
in the form
q(x)+\frac{r(x)}{d(x)}
5x^2-2x-3+(10x-3)/(x^2+2)
Find all real zeros.
2x^3-5x^2-28x+40=0
x≈-3.384, x≈1.285, x≈4.599
Find all zeros of
f(x)=x^4+x^3-2x^2+4x-24
(Be sure to include complex solutions.)
x= -3, 2, 2i, -2i
Solve the rational inequality
(x+4)/(x-1)<0
Solve
27^(x+1)=9^(2x)
x=3
An investment of $12,000 earns 6% annual interest compounded quarterly. How much will it be worth after 8 years. Round ti the nearest cent,
$19,295.79