The polynomial p(x)=x^3+7x^2-36p(x)=x 3 +7x 2 −36p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 7, x, squared, minus, 36 has a known factor of (x+3)(x+3)left parenthesis, x, plus, 3, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p(x)=
Answers
Answer:
(x-2)(x+3)(x+6)
Step-by-step explanation:
Given the polynomial function p(x)=x^3+7x^2-36
We are to write it as a product of its linear factor
Assuming the value of x that will make the polynomial p(x) to be zero
Let x = 2
P(2) = 2³+7(2)²-36
P(2) = 8+7(4)-36
P(2) = 8+28-36
P(2) = 0
Since p(2) = 0 hence x-2 is one of the linear factors
Also assume x = -3
P(-3) = (-3)³+7(-3)²-36
P(-3) = -27+7(9)-36
P(-3) = -27+63-36
P(-3) = 36-36
P(-3) = 0
Since p(-3) = 0, hence x+3 is also a factor
The two linear pair are (x-2)(x+3)
(x-2)(x+3) = x²+3x-2x-6
(x-2)(x+3) = x²+x-6
To get the third linear function, we will divide x^3+7x^2-36 by x²+x-6 as shown in the attachment.
x^3+7x^2-36/x²+x-6 = x+6
Hence the third linear factor is x+6
x^3+7x^2-36 = (x-2)(x+3)(x+6)
Answer:
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
Step-by-step explanation:
Here we want to rewrite the polynomial
P(x) = x^3 + 7x^2 - 36
As a product of linear factors given that we have one of the roots already as (x + 3)
What we shall do here is to divide the polynomial by x + 3
Please check attachment for long polynomial division
From the division, the other factor is x^2 + 4x -12
So we can rewrite the polynomial as;
x^3 + 7x^2 -36 = (x + 3)(x^2 + 4x -12)
So let’s now write x^2 + 4x -12 as a product of its linear factors
x^2 + 4x -12 = x^2 + 6x -2x -12
= x(x + 6)-2(x + 6)
so we have;
(x -2)(x + 6)
Therefore;
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
Related Questions
The ocean exploration institute has a submarine that is used to study patterns of fish moment the submarine started at the surface of the water and collected data at three different depths each time the submarine dove 40 feet down write an integer equation to model the situation and determine the lowest depth of the submarine
Answers
Answer:
120 feet
Step-by-step explanation:
Given that the submarine started at the surface of the water and collected data at three different depths.
As each time the submarine dove 40 feet down, so,
the depth covered in one dive = 40 feet.
From the surface, the depth covered in 1 drive, [tex]d_1= 40[/tex] feet
Similarly, the total depth covered in 2 drive, [tex]d_2 = 2\times 40= 80[/tex] feet.
So, for any integer [tex]n[/tex], the depth covered in [tex]n[/tex] drive,
[tex]d_n=40n[/tex]
This is the required integer equation to model the situation.
Since, for three different depths, there must be 3 drive and the submarine will be at the lowest depth after 3rd dive.
So, for the lowest depth, n=3
Hence, the lowest depth = 40x3= 120 feet.
The perimeter of a rectangle is 70cm. If the length of the rectangle is 5cm more than its breadth, find the dimensions of the rectangle.
Plsss help I put 15 points
Answers
Hope it helps man .....
Estimate the sum 78.5+51.4
Answers
Answer:
129.9
Step-by-step explanation:
78.5
+ 51.4
129.9
Hope this helps! (:
Simplify 9 to the 2nd power/ 9 to the 7th power
Answers
Answer:
9^2=81, 9^7=478,296,9
You work in a grocery store warehouse recording shipments. A driver delivers 25 crates of strawberries for distribution. A store calls needing seven crates of strawberries. After you fill this order, how many crates of strawberries are available for other stores?
Answers
Answer:
18 crates
Step-by-step explanation:
Data provided in the question
The Number of strawberries for distribution delivered is 25 crated
Now he seven crates is required
So the remaining crates left is
= 25 - 7
= 18 crates
hence, after filling the order the number of order crates of strawberries is 18 crates and the same is to be considered
What is the value of x?
Answers
Answer:
As x is the exterior angle
Step-by-step explanation:
therefore
let name the angle exterior angle be ACE
interior angleABC=76°and angleBAC=55°
sum of 2 interior angle is equal to exterior angle
=76+55=x
=131=x
PLEASE ANSWER!! Quadrilateral PQRS is shown on the coordinate plane.
Answers
Answer:
i have no idea
dont spam "please answer" its not cool
find the slope of the line passing through the points (-2,-8) and (7,-8)
Answers
Answer: 0/9
Step-by-step explanation: Hi there!
First, we have to put the points into the y2-y1/x2-x1 form.
Take the y value from the second point (-8) and the first point y value (-8)
and subtract.
-8 - (-8)
to get 0
Now we have to get our denominator by taking the x value from our second point and subtracting it by our first y point.
7 - (-2)
to get 9
so when we put that together...
we get 0/9
So the answer is 0/9.
Hope this answer helps you!
According to a company's website, the top 15% of the candidates who take the entrance test will be called for an interview. You have just been called for an interview. The reported mean and standard deviation of the test scores are 70 and 7, respectively. If test scores are normally distributed, what is the minimum score required for an interview?
Answers
Answer:
The minimum score required for an interview is 77.252
Step-by-step explanation:
We solve this using z score formula
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Top 15% of the candidates is a ranking that is equivalent to = 100 - 15% = 85th percentile.
The z score of 85th percentile = 1.036
Mean = 70
Standard Deviation = 7
Minimum score = raw score = ???
Hence:
1.036 = x - 70/7
Cross Multiply
1.036 × 7 = x - 70
7.252 = x - 70
x = 70 + 7.252
x = 77.252
The minimum score required for an interview is 77.252
How can you use linear relationships to compare real-world
situations?
Answers
Answer:
Linear equations use one or more variables where one variable is dependent on the other. Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit.
Step-by-step explanation:
Solve for m: 2m + 5-3m = 7
Answers
Answer:
m=-2
Step-by-step explanation:
Answer: m = -2
Step-by-step explanation:
Simplify 2m + 5 - 3m to -m+ 5
-m + 5 = 7
Regroup terms.
5 - m = 7
Subtract 5 from both sides.
-m = 7 - 5
Simplify 7 - 5 to 2
-m = 2
Multiply both sides by -1
m = -2
A girl’s club held a fundraiser last year and raised $600 for the local soup kitchen. This year they raised $960. What is the percent change in the total amount raised by the girl’s club?
The percent change is 0.38%.
The percent change is 0.6%.
The percent change is 38%.
The percent change is 60%.
Answers
Answer: option D
Step-by-step explanation:
Answer:
D.) The percent change is 60%
Step-by-step explanation:
I know this because 960-600= 360
360÷600= .6
.6= .60
.60= 60%
Hope this helped!!! :)
Please help im a bit confused
Answers
Answer:
200,000
80,000
9,000,000
10,000,000,000
What is the context of this question?
Step-by-step explanation:
Answer:
So standard form just means 200,000 written as like 200^ something(I think)
Step-by-step explanation:
Melissa shot a rocket 360 meters into the air, it took 4 seconds to fly that far. What’s the average speed of the rocket?
Answers
Answer:90meters per second
Step-by-step explanation:
8 to the 4th power times 2 divided by 8 to the eleventh power
Answers
Answer:
17179869191.3 (really i used a calculator, it was too hard)
Step-by-step explanation:
8^4 is 4096
2/8 is .25
.25^11 is 2.38418579e-7
4096/2.38418579e-7
17179869191.3
1/3 of the 12 pencils were broken.How many pencils were broken
Answers
Answer:
4
Step-by-step explanation:
You can multiply 1/3 by 4 to equal 12 giving you your answer
Answer:
Step-by-step explanation:
4 pencils were broken
1/3 * 12 is 4
Choose the definition, theorem, or postulate that justifies the statement.
A. Definition of a Right Angle
B. Definition of Complementary Angles
C. Congruent Complements Theorem
D. Complement Theorem
E. Definition of Supplementary Angles
F. Definition of Angle Bisector
G. Supplement Theorem
H. Definition of Perpendicular
I. Angle Addition Postulate
J. Vertical Angles Theorem
K. Congruent Supplements Theorem
L. Definition of Congruence
Answers
Answer:
its b i got it correct
Step-by-step explanation:
on ed 2020
Evaluate 6x – y if x = 5 and y = 8.
3
22
43
57
Answers
Answer:
the answer is 22
Step-by-step explanation:
you just need to plug in the values of x and y so...
6(5)-8
30-8
=22
A function f(x) is graphed.
What is the slope of the function?
ma
What is the y-intercept of the function?
b.
Which equatich represents the graph of the function?
Answers
Answer:
slope:1/2
y intercept:-1/2
equation of the line: y=1/2x-1/2
Step-by-step explanation:
choose two points from the line( I chose (3,1) and (-1,-1)) and then using y1-y2/x1-x2, do 1 - -1/3 - -1 which is 2/4 simplified to 1/2. the slope is 1/2.
now to find the y intercept, you just have to plug in the numbers from one of the sets of points you chose and your slope using y = mx +b(I will be using the point (-1,-1)). equational look like this: -1=1/2•-1+b
since b is the y intercept, solve for b and you get b= -1/2.
so nowsince you know the slope and the y intercept you just plug it in to the equation
y = mx + b and you get y=1/2x-1/2.
DUE TODAY AT 12! PLS HELP ALGEBRA WILL GIVE BRAINLIEST!
Answers
Answer:
Im gonna go with b not 100% tho
Step-by-step explanation:
original cost 14.50 markup:14%
Answers
Answer:
Step-by-step explanation:
Use the given functions to set up and simplify
14%. 14.5 = 14% = 0.14
Jordan doesn't know how to graph y > 2x + 1 . Can you explain to him using the words below how to do it?
Vocabulary to use:
slope, y-intercept, shade above/below, and dotted/solid line
Answers
Answer:
Step-by-step explanation:
Formula: Y= mx+b
m = slope | b = y-intercept
Equation: Y>2x+1
The Y-Intercept is the (1)
Shade above the dotted line because it is >.
You always shade on the left if the left side of the equation is > than the right.
If ≥ Then the line is Solid |||| If > Then the line is dotted.
simplify the following
Answers
Answer:
D. 64 z^ 2
Step-by-step explanation:
Simplify the expression.
Three ice cream cones cost $8.40. At this rate, how much do two ice cream cones cost?
Answers
Answer:
two cost 5.6 dollars
Step-by-step explanation:
8.4 / 3=2.8$
2.8*2=5.6$
Answer:
$5.60
Step-by-step explanation:
You first take 8.40 and divide it by 3. Which makes you get 2.8. 2.8 is the cost per ice cream cone. Do 2.8 times 2 to get 5.6.
On a certain Friday night, the local baseball stadium earned $867.50 in revenue from ticket sales on 310 tickets. Ticket prices are $3.00 for adults and $2.50 for children. How many adults attended the game on Friday?
Answers
Answer:
185
Step-by-step explanation:
Found by solving the system of equations:
3x+2.5y = 867.5
x+y = 310
List the following in order from least to greatest 20,2-2,(-2)2,-22
Answers
Answer:
(-22) ,- (2)2 , 2-2 , 20
Step-by-step explanation:
negative then postive
20
2-2=0
(-2)*2=(-4)
-22
hope this helps :)
brainliest?
Write the inequality:
2 times d is less than 10
Answers
Answer:
2d<10 or 10>2d
Step-by-step explanation:
Answer:
2d < 10
Step-by-step explanation:
Which of the following is equivalent to 5(7 - p)?
5p - 35
-5p + 35
35 + 5p
-35 + 5p
Answers
Answer:
-5p+35
Step-by-step explanation:
=(5)(7+−p)
=(5)(7)+(5)(−p)
=35−5p
=−5p+35
A 2-pound bag of sugar contains 227 one-teaspoon servings and costs $2.49. A batch of muffins uses 1 2 cup of sugar. How many whole batches can you make if you use as much of the sugar as possible? What is the cost of sugar for each batch? (1 cup = 48 teaspoons; do not consider leftover sugar in the cost calculation.) You can make a total of batches at $ per batch.
Answers
Answer:
a) 9 whole batches can be made
b) The cost of sugar for each batch = $0.26
Step-by-step explanation:
A 2-pound bag of sugar contains 227 one-teaspoon servings and costs $2.49.
This means:
2 pound bag of sugar = 227 teaspoon servings
2 pounds bag of sugar cost $2.49
We are told that:
A batch of muffins uses 1/2 cup of sugar.
a).How many whole batches can you make if you use as much of the sugar as possible?
(1 cup = 48 teaspoons)
Hence, A batch of muffins = 1/2 cups of sugar = 48 teaspoons of sugar ÷ 2
= 24 teaspoons of sugar
Hence:
24 teaspoons of sugar = 1 batch of muffins
227 teaspoons of sugar = x
Cross Multiply
24 × x = 1 × 227
x = 227/24
x = 9.4583333333 batches of muffins
We are asked to name the number of whole batches that can be made.
Therefore, 9 whole batches of muffins can be made
b) What is the cost of sugar for each batch? (do not consider leftover sugar in the cost calculation.) You can make a total of batches at $ per batch.
Since we are not to consider the leftover sugar in the cost calculation,
1 batch = 24 teaspoons of sugar
9 whole batches =
9 × 24 teaspoons = 216 teaspoons of sugar was used
The left over = 227 - 216 = 11 teaspoons of sugar is left
We know that:
227 teaspoons of sugar = $2.49
216 teaspoons of sugar = x
Cross Multiply
= 216 × $2.49/227
= $2.369339207
24 teaspoons of sugar = 1 batch of muffins
Therefore,
216 teaspoons of sugar =
$2.369339207
24 teaspoons of sugar =
24 × $2.369339207/ 216
= $0.2632599119
Approximately = $0.26
Therefore, the cost of sugar for each batch = $0.26
Linda bought n packs of pencils. Each pack has 12 pencils. Write an equation to represent the total number of pencils p that Linda bought.
Answers
Answer:
p = 12n
Step-by-step explanation:
Given parameters:
Number of pencils in each pack = 12 pencils
Number of packs bought = n
Unknown:
equation for total number of pencils, p = ?
Solution:
Total number of pencils = number of pencils in each pack x number of packs bought
Input parameters:
p = 12 x n
p = 12n