Answers
Answer:
The quotient when [tex]x^3-4x^2-8x+8[/tex] is divided by [tex]x+2[/tex] is [tex]x^2-6x+4[/tex] with no remainder, so x+2 is a factor of p(x).
Step-by-step explanation:
As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form [tex](x-a)[/tex]. In this case, we may use synthetic division, since [tex]x+2[/tex] is equal to [tex]x-(-2)[/tex]. I will use synthetic division here as it is slightly faster than long division.
The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.
The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.
Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.
This is the answer: the quotient is [tex]x^2-6x+4[/tex], and the remainder is zero (which indicates that x+2 is a factor of p(x)).
--
Edit: long division
We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since [tex]x \times x^2[/tex] is equal to [tex]x^3[/tex], the first term in the quotient will be [tex]x^2[/tex]. Since [tex]x^2 \times (x+2)[/tex] is equal to [tex]x^3+2x^2[/tex], we must now subtract that from [tex]x^3-4x^2-8x+8[/tex].
We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.
I know this might be difficult to follow, so please comment if you have any questions.
Related Questions
SOMEONE HELP ASAP PLS!!
Point K lies at (-3,4). Point K is reflected over the y-axis and then translated 7 units down to produce K'. Which rule could have been used to produce K’ from K?
Answers
K(x,y)>K’(-x,y-7)
Answer:
K(x,y) →K'(-x, y-7) (B)
Step-by-step explanation:
4x - 2y = 5 and y = 3x - 1
Answers
Answer:
4x_2y=5
4x=5+2y
x=5+2y/5
now, y=3x_1
putting value of x in second question
In this way you can do
A telephone marketer earns a 14% commission on their sales each week. In one week, their sales amounted to $920.
1a
First, find 10% of their total sales.
Answers
Answer:
I love u plz don't report
Please help. If this isn't done by today i'm grounded :(
A _____ magnet can be made by rubbing a permanent magnet the same way
along an item. The alignment of atoms does not last long.
permanent
temporary
atomic
polar
Answers
Answer:
B. temporary
Step-by-step explanation:
The last sentence says that the alignment of atoms does not last long.
Answer:
B. temporary
Step-by-step explanation:
You bought a can of black beans last week that cost $1.34. This week, the store advertised a sale where 5 cans of beans cost $6.00. You bought one can of beans this week as well. Find the cost per can, and determine how much less the can of beans cost this week compared to last week.
Answers
Answer:
1. $1.2
2. $0.14
Step-by-step explanation:
Step one:
given data
Black beans last week that cost $1.34
Step two:
This week's price
5 cans of beans cost $6.00
The cost per can is
= 6/5
=$1.2
The difference in price
=1.34-1.2
= $0.14
If t= 9m,what is the area of the triangle
Help
Answers
Answer: the answer
we use the formula 1/2 .b .h
Step-by-step explanation:
the answer is 1,134, we substitute the t to 9 for each number, for example 4(9) 7(9)
4(9)= 36
7(9)=63
now we find the half of our bottom number which is 4=36
1/2 36= 18
so now we have 18x63=1,134
so our answer is 1,134
The area of the triangle is 1134 m²
What is the area of Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
Given data ,
The value of t = 9 m
Let the base of the triangle be b = 4t
= 4 x 9
= 36 m
Let the height of the triangle be h = 7t
= 7 x 9
= 63 m
Now , the area of the triangle = ( 1/2 ) x Length x Base
So , substituting the values , we get
Area of the Triangle = ( 1/2 ) x 36 x 63
= 18 x 63 m²
= 1134 m²
Therefore , the area is 1134 m²
Hence , the area of the triangle is 1134 m²
To learn more about area of triangle click :
https://brainly.com/question/20124564
#SPJ5
How do you solve this?
Look at attached file please...I'm really confused!
Answers
Answer:
X=18, Y=6
Step by Step Explanation:
This is a little long winded.. Let's solve for Y first.
First looking at the problem, you can note a few things. First of all, there is an Isosceles triangle, and there is an equilateral triangle. Where they connect, there is a 90° angle.
Now, all equilateral triangles have the same angle measurement. 60°. Now, if you look where the right angle is, it is showing a 60° angle, a total of 90°, and an unknown area. So simply subtract. 90-60=30. Divide that by 5, and you have your answer of 6.
Now let's solve X. X is very simple. On an isosceles triangle, the two top sides are the same length. And one of the top sides is the same size as the equilateral triangle. And on equilateral triangles, all sides are the same.
So the 11 transfers over to the X side. So let's make a small equation. 11=X-7. To make it even, let's add 7 to both sides. 11+7=X+7-7. Simplify to get 18=X, which is your answer.
Answer:
X=18 y=6
Step-by-step explanation:
explain and solve
Find the midpoint of the line segment with the given endpoints.
(-10,-4), (6,-5)
Answers
-10+6 = -4/2 = -2
-4 - 5 = -9/2 = -4.5
Solution: (-2, -4,5)
Use the order of operations to evaluate this expression: 7 + (5 – 9)2 + 3(16 ÷ 8).
Answers
Answer:
= 7 + (5 – 9)2 + 3(16 ÷ 8)
= 7 + (-4)2 + 3(2)
= 7 + (-8) + 6
= -1 + 6
= 5
Step-by-step explanation:
Remember to use PEMDAS when solving.
the ratio of boys to girls in a class is 4 : 5 how many girls are there in a class if 12 boys are in the class
Answers
Answer:
15
Step-by-step explanation:
Hey! Pretty stranger :D
AsnwEr:
Number of girls in class = 15GivEn:
The ratio of no. of boys to no. of girls in a class is 4:5.Number of boys in class = 12To find:
Number of girls in class?Solution:
☯ Let number of girls be x.
Given that,
The ratio of no. of boys to no. of girls in a class is 4:5.Therefore,
→ 12/x = 4/5
→ x = 12 × 5/4
→ x = 60/4
→ x = 15
∴ Hence, number of girls in a class is 15.
HELP MEEE PLEASEEEEE!!!!! I NEED HELPPP!!
Which the ordered pair that is a solution of the system for linear equations?
Answers
Answer:
(2,2)
Step-by-step explanation:
Lets check:
(2,2)
2(2)-2=2 Correct !
2=-2+4 correct !
Hope this helps plz hit the crown :D
Answer:
i believe the answers (2,2)
Step-by-step explanation:
if you add it in for y and x you will see it right
Help pls help me!!!!!
Answers
Answer:
C
Step-by-step explanation:
This is your answer because when you do the math you get c as your answer.
Hope this help:)
pls mark brainly
Answer:
The answer is C
Step-by-step explanation:
You had $72.31 at the beginning of the month but you deposited $11.27 and $14.76 so if you add all of those you get $19.84
Have a great day!
Please consider marking brainliest
^-^
What is 0.00015 in scientific notation?
Answers
Answer:
1.5 * 10^(-4) is the scientific notation.....
Hello' this is my last question can someone please help me
(please don't just put a random answer just to take my points)
Answers
*puts a random answer just to take your points*
JK lol sorry
Answer~If we are solving for x, then your answer would be
8x²~x = 0.110
10x~x = 1.140
How i did it~first x:[tex]\frac{10-\sqrt{68} }{16} = \frac{5-\sqrt{17} }{8}[/tex] =0.110
second x:[tex]\frac{10+\sqrt{68} }{16} = \frac{5+\sqrt{17} }{8}[/tex] =1.140
------------------------------------------------------------------------hope I helped :P
Have a good day!!~
Evaluate 1/2t + 3/8 when t= 1/4
Answers
Answer:
1/2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
1/2t + 3/8
t = 1/4
Step 2: Evaluate
Substitute: 1/2(1/4) + 3/8Multiply: 1/8 + 3/8Add: 4/8Simplify: 1/21/8 + 3/8 = 4/8 or 1/2
So the answer is 1/2
Hope I helped
Olivia filled 4 baskets of apples. Her friend filled up one additional basket of apples. if all of the baskets sold for a total of $160, how much money did each basket of apples cost?
Answers
Answer:
$32
Step-by-step explanation:
Since the question says that all the apples were sold for a total of $160, this means that you have to add the additional basket of the friend's to Olivia's. Since Olivia has 4 baskets of apples and her friend has 1, 4+1=5. Since you're trying to find the unit price for 1 basket, you take the total of $160 and divide it by 5 to find how much each basket of apples costed. Since 160/5 is 32, $32 is your answer.
Comparing Functions
How much money will Bob in December have if his bank account growth stays at the same rate?
Month Bank-Acc
|
January | $5,000
February $6,700
March $8,400
April $10,100
May $11,800
Answers
if I have a 40 in a class and get 100% on something thats 40% of my grade. whatsmy new grade PLEASE ANSWER like please please please please answer
Answers
Answer: depends on how your class is weighted, and specifically how many points the thing is, and your point score.
Step-by-step explanation:
i guess 60%? it's too vague
find the slope of the line y=-3/8x-7/6
Answers
Answer:
The slope is -3/8
Step-by-step explanation:
Y= mx+b
m or mx is the slope while b is the y intercept
The answer. X=7 Ik that
Answers
Answer:
C: 147°
Step-by-step explanation:
Based on looking, the most appropriate answer should be C, which is 147°.
what slope of line passess through 4,1 and -2,-4
Answers
Answer:
A slope..... I can't do math
Step-by-step explanation:
10x^3-35x^2 please help me
Answers
Answer:
5x^2(2x-7)
Step-by-step explanation:
Hope this helps!
the ratio of white socks to brown socks is
PLZ HELP ASAP
Answers
Answer:
0.875 is the ratio from white to brown socks.
Does the blue on the graph represent a function ?
Answers
Answer:
Nope
Step-by-step explanation:
It doesnt. Functions look like that
explanation:
I NEED HELP ASAP IN THE PICTURE ABOVE
Answers
Answer:
Step-by-step explanation:
Even numbers are those that can be divided by 2.
3440 and 7802
Odd numbers are the rest
4893, 1451 and 6645
Smallest to largest
1451, 3440, 4893, 6645 and 7802
Sum of even numbers
3440+7802= 11242 divided by 2(there are only 2 numbers)
11242 ÷ 2 = 5621
Jake has 3 1/2 hours before bedtime. He must spend 2 hours doing homework. The rest of his time will be spent doing puzzles. It takes jake 1/2 hour to complete each puzzle. Which equation models the number of puzzles, p, jake can complete before bedtime?
Answers
Explanation: p is number of puzzles
Answer:
3 1/2 puzzles
Step-by-step explanation:
Write each fraction as a percent.
8/20
Answers
Answer:
40%
Step-by-step explanation:
8/20=0.4
0.4=40%
Solve for x
(I’ve tried everything I can think of, but I still haven’t been able to solve this. Please help!)
Answers
Answer:
x = 6
∠2 = 75
Step-by-step explanation:
In the given triangle two sides are equal and so it is an isosceles triangle. So, the angles opposite to equal sides are equal
11x + 9 + 11x + 9 + 30 = 180 {Angle sum property of triangle}
11x + 11x + 9 +9 +30 = 180
22x + 48 = 180
22x = 180 - 48
22x = 132
x = 132/22
x = 6
∠2 = 11*6 + 9 = 66 +9 = 75
at an amusement park, children are charged an entrance fee of $20 plus $3 per ride and adults are charged an entrance fee of $28 plus $4 per ride. Identify your variable with a 'let' statement and write expressions for both children and adults that represent the cost for each group.
Answers
Answer:
T=3r+20 for the children and T=4r+28 for the adults
Step-by-step explanation:
Let r equal the amount of rides the person took, let T equal the total cost of the trip
Simplify (-2x - 9)(-4). 8x - 36 -8x + 36 8x+ 36 -88-36
Answers
Answer:
8x+36
Step-by-step explanation:
distribute the -4
-2x times -4 + -9 times -4
8x+36
xoxo, your highness...Answer:
[tex]64x^2+648x-124[/tex]
if your question is
[tex]\left(-2x-9\right)\left(-4\right)\cdot \:8x-36-8x+368x+36-88-36[/tex]