(01.02 MC)
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
Answers
The function is given by: h(x) = -2(x³ - 2x² - 5x + 6).
What is meant by Factor Theorem?The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has this particular special instance. A polynomial f(x) has a factor if and only if f=0, according to the factor theorem.
The Factor Theorem states that a polynomial function with roots [tex]$x_1, x_2, x_n$[/tex] is given by:
[tex]$$f(x)=a\left(x-x_1\right)\left(x-x_2\right) \cdots\left(x-x_n\right)$$[/tex]
In which a is the leading coefficient.
Looking at the table, considering the values of x when h(x)=0, the roots of h(x) are given as follows:
[tex]$$x_1=-2, x_2=1, x_3=3$$[/tex]
Then the rule is:
h(x) = a(x + 2)(x - 1)(x - 3)
h(x) = a(x² + x - 2)(x - 3)
h(x) = a(x³ - 2x² - 5x + 6)
The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:
6a = -12
simplifying the above equation, we get
a = -12/6
a = -2.
Therefore, the function is given by: h(x) = -2(x³ - 2x² - 5x + 6).
To learn more about Factor Theorem refer to:
brainly.com/question/24380382
#SPJ1
Related Questions
Santino pays $36.85 for eleven 10-count boxes of granola bars. How much does 1 box of granola bars cost?
Answers
Answer:
One box of granola bars costs $3.35.
Step-by-step explanation:
36.85/11=3.35
Which of the following is a rational number? Select all that apply.
A. √1
B. √3
C. √4
D. √5
E. √8
F. √9
Answers
Answer: The numbers that are rational numbers are A, C, and F.
Step-by-step explanation: This is because all non-perfect square roots are always irrational. Also, perfect square roots are always RATIONAL. Therefore, the rational numbers of the choices given are [tex]\sqrt{1} , \sqrt{4}, \sqrt{9}[/tex]
Answer: A, C, and F. √1 √4 √9
Write the linear equation in slope-intercept form given the following:
(-3, 7) and (6, -8)
Answers
Answer:
y = - [tex]\frac{5}{3}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 7) and (x₂, y₂ ) = (6, - 8)
m = [tex]\frac{-8-7}{6+3}[/tex] = [tex]\frac{-15}{9}[/tex] = - [tex]\frac{5}{3}[/tex] , then
y = - [tex]\frac{5}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (6, - 8) , then
- 8 = - 10 + c ⇒ c = - 8 + 10 = 2
y = - [tex]\frac{5}{3}[/tex] x + 2 ← equation of line
Susan graphed a system of equations for the lines y = 3x + 1 and y = 3x - 10. Which statement is true about Susan's lines?
The lines intersect once at a right angle because they are perpendicular.
The lines intersect at all points because they are the same line.
The lines intersect three times because each has a slope of three.
The lines do not intersect because they are parallel and have different y-intercepts.
Answers
Answer: The lines do not intersect because they are parallel and have different y-intercepts.
Step-by-step explanation:
PLS PLS HELP ASAP I WILL MARK BRAINLIEST
Using the given equation find the missing coordinates of the points and then find the slope of the line for the equation.
y=3.5x+4; A(...;5), B(10;...)
Answers
Okay so,
A (0.2875; 5), B (10; 39)
THE SLOPE IS 3.5
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
7j2 + 3j2 + j?
Answers
Answer:
10j^2 +j
Step-by-step explanation:
I added the first two terms since they have the same exponent and then left the j because its not squared or anything
PLEASE HELP URGENT
Hank's age is 5 more than three times John's age. Hank
is 29 years old. How old is John?
Answers
A cone has a volume of 47.1 cm³ and a radius of 3 cm what is its height?
Answers
Radius of cone ( r ) = 3 cm,
Curved surface area of a cone= 47.1 cm²
Curved surface area of a cone= πrl
47.1 = πrl
47.1 = 3.14 × 3 × l
l = 47.1 / (3.14 × 3)
l = 15.7 / 3.14= 1570/314= 5 cm
slant height (l) = 5 cm
Height of a cone (h) = √(l²) - (r²)
h = √ 5² -3²
h = √ 25 - 9 = √ 16 = 4 cm
h = 4 cm
Volume of cone= ⅓(πr²h)
= ⅓(3.14 × 3 × 3 × 4)
= 3.14 × 12= 37.68 cm³
Hence, the volume of a cone is 37.68 cm³.
Are 0.34 and 3/4 equivalent? Please explain your answer In complete sentences.
Answers
when 3 divided by 4 is converted into a decimal, it is 0.75 which does not equal 0.34
0.34 can also be written as 34/100
and 3/4 can be written as 75/100
therefore 0.34 and 3/4 are not equivalent
Decide wether the function is linear or nonlinear.
Linear function
Nonlinear function
Answers
it does not follow a constant rate of change
broooo plzzz helpppp
Answers
Answer:
3 3/5 + 1 1/4 = 4 17/20
7/8 + 1/12 = 23/24
8/9 - 2/5 = 22/45
5 1/4 - 2 2/3 = 2 7/12
Step-by-step explanation:
3 3/5 + 1 1/4
First convert into improper fractions
= 18/5 + 5/4
Now find the common denominator
72/20 + 25/20 =
97/20
Now simplify
4 17/20
Next problem:
7/8 + 1/12
find the common denominator
21/24 + 2/24 =
23/24
Next problem:
8/9 - 2/5
find the common denominator
40/45 - 18/45 =
22/45
Next problem:
5 1/4 - 2 2/3
First convert into improper fractions
21/4 - 8/3
find the common denominator
63/12 - 32/12 =
31/12
Now simplify
2 7/12
It took Hank 3.4 hours to travel 124 miles. At that rate, how long will it take Hank to travel 310 miles?
Answers
Answer: Time = 8.5 hours
Step-by-step explanation:
Step 1
Speed = distance / time
Distance traveled by Hank = 124 miles
Time = 3.4 hrs
Speed= Distance / Time
= 124/ 3.4 = 36.47 miles per hour
Step 2
At this same rate of speed =36.47 miles per hour, if he travels 310 miles, he will spend=
Time = Distance / Speed
Time = 310/ 36.47
Time =8.5 hours
Solve for n:
1-5|n-9|=-74
I need answer by 12:10, please help!!!
Answers
Answer:
[tex]n=-6, 24[/tex]
Step-by-step explanation:
We are given:
[tex]1-5|n-9|=-74[/tex]
Subtract 1 from both sides:
[tex]-5|n-9|=-75[/tex]
Divide both sides by -5:
[tex]|n-9|=15[/tex]
By definition of absolute value:
[tex](n-9)=15\text{ or } -(n-9)=15[/tex]
Solve for each case:
[tex]n=24\text{ or } n=-15+9=-6[/tex]
Therefore, our two solutions are:
[tex]n=-6, 24[/tex]
There are three rows of VIP seats in each section. Each row
has 12 seats and there are 16 sections. How many VIP seats
are there in all?
Answers
Answer:
The answer is 576 seats
Step-by-step explanation:
3 rows x 12 seats = 36 seats in one section
36 seats in one section x 16 sections = 576 seats
How do I write a phrase in words as an algebraic expression for 8/d?
Answers
Answer:
The quotient of 8 and d.
Step-by-step explanation:
I hope this helps you have a wonderful day! :D
On a certain hot summer's day, 234 people used the public swimming pool. The
daily prices are $1.25 for children and $2.00 for adults. The receipts for admission totaled
$435.00. How many children and how many adults swam at the public pool that day?
Answers
Step-by-step explanation:
2/3z=-6
Help please!!
Answers
Answer:
z = -9
Step-by-step explanation:
I need help plz......I'll give brainliest:
The sum of two numbers is 44. The smaller number is 12 less than the larger number. What are the numbers?
Answers
x+(12+x)=44
2x+12=44
2x=32
x=32/2
x=16
The two numbers are 16, 28
Hope I helped :)
(Look at photo for reference)
Answers
Answer:
B
Step-by-step explanation:
6% is usually represented by 0.06
Hope this helped :)
choose the answer that represents the product below as an exponential expression*
Answers
Answer:
B
Step-by-step explanation:
the bases are the same and according to exponential laws exponents of the same base are added
Answer:
B
Step-by-step explanation:
A spinner has 3 sections of different sizes. The sections are orange, purple, and green. 1/4 of the spinner is orange. 7/12 of the spinner is purple. Which fraction of the spinner is green?
Answers
Answer: it would be 2/3
Step-by-step explanation:
if 2x + 16 = -6x what is x
Answers
Answer:
x = -2
Step-by-step explanation:
Answer:
x is -2
Step-by-step explanation:
8x+16=0
subtract 16 from both sides
8x=-16
Divide each term by 8 and simplify
x=-2
Radium-226 has a half-life of 1660 years. How many years does it take a radium sample to decay to 55% of the original amount? Round your answer to the nearest year.
Answers
Answer:
1432 years
Step-by-step explanation:
A(t) = I(0.5)^t/t1/2
Where t1/2 = half life = 1660
Final amount, A(t) = 0.55 of its original amount =. 0.55I
Hence, we have
0.55I = I(0.5)^t/1660
Take the log of both sides
Log(0.55) = log(0.5)^t/1660
t/1660 = log(0.55) / log(0.5)
t/1660 = 0.8624964
t = 0.8624964 * 1660
t = 1431.7441
t = 1432(nearest whole number)
Find the missing length indicated.
Pls Help
Answers
What is the multiplicative rate of change for the exponential function f(x)= 3 (2/3)^-x
A. 0.4
B. 2.5
C. 0.6
D. 1.5
Answers
Answer:
C basta Yan ang sagot HAHAHA dko mapicturan solution ko e
Step-by-step explanation:
ano ba yan arte nyo sabing yan ang sagot eAnswer:
c 0.6
Step-by-step explanation:
lol
Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?
(1, –1)
(0, 0) and (0, –1)
(0, 0) and (2, 0)
no solutions
Answers
Answer:
D) no solutions :D
If the cos 90° = 0, then the sin 0° = _____.
pls help
Answers
Answer:
I think its 0
Step-by-step explanation:
Answer:
This one too clicked by me
I need help getting started
Answers
2.-7/6
3.3/4
4.-1/4
5.-5/4
6.-1/2
7.-3/4
8.-5/3
what are all the sums and differences of 3/4?
Answers
Answer:
1/2 + 2/4
11/12 - 1/6
3/5 + 3/20
7/8 - 1/2
Step-by-step explanation:
what is the median of 9.3 an 6.8?????
Answers
Answer:
Désolé mec mais je n'ai pas compris ta question