(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
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
2/3z=-6
Help please!!
Answers
Answer:
z = -9
Step-by-step explanation:
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:
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 :)
what is the median of 9.3 an 6.8?????
Answers
Answer:
Désolé mec mais je n'ai pas compris ta question
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
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]
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
(Look at photo for reference)
Answers
Answer:
B
Step-by-step explanation:
6% is usually represented by 0.06
Hope this helped :)
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
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
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:
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:
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
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.
Find the missing length indicated.
Pls Help
Answers
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)
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
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
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:
Decide wether the function is linear or nonlinear.
Linear function
Nonlinear function
Answers
it does not follow a constant rate of change
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
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
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
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
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:
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
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