Answer:
How does knowing one linear factor of a polynomial help find the other factors?
Step-by-step explanation:
f(x)=(x−3)(x−1)(x+2)(x+6)
f(x)=(x−2)(x−2)(x+3)(x+5)
f(x)=(x−5)(x−3)(x+2)(x+2)
f(x)=(x−8)(x−1)(x+3)(x+5)
f(x)=(x−2)(x−1)(x+4)(x+4)
Correct answer:
f(x)=(x−2)(x−2)(x+3)(x+5)
Explanation:
We begin by attempting to find any rational roots using the Rational Root Theorem, which states that the possible rational roots are the positive or negative versions of the possible fractional combinations formed by placing a factor of the constant term in the numerator and a factor of the leading coefficient in the denominator.
That was a lot of wordage in one sentence, so let's break that down. We begin with our polynomial.
f(x)=x4+4x3−13x2−28x+60
The constant term is the term without a variable (just a plain number). In our case the constant is 60. What are the possible factors of 60?
1,2,3,4,5,6,10,12,15,20,30,60
The leading coefficient is the number in front of the largest power of the variable. When the terms are listed in descending order (highest to lowest power), the leading coefficient is always the first number. In our case the leading coefficient is hard to spot. Since there is no number in front of x4, the coefficient is 1 by default.
This is nice because the only factor of 1 is well ... 1.
We then create all the possible fractions with a factor of the constant in the numerator and a factor of the leading coefficient in the denominator. This actually isn't as bad as it could be since our only possible denominator is 1. Any fraction with a denominator of 1 is just the numerator. Therfore, our possible "fractions" are simply
1,2,3,4,5,6,10,12,15,20,30,60
However, we must consider the positive or negative versions of these, so our final list of possible rational roots is
±1,±2,±3,±4,±5,±6,±10±,1±2,±15,±20,±30,±60
Unfortunately, this is where the process (at least without the assitance of a graphing calculator) becomes less fun. Using synthetic division, we must simply try each possible root until we have success. There's really no consistent rule to tell us where to start. Generally starting with the smaller whole numbers is best because the synthetic division is easier. Therefore, we could begin with 1 then proceed to −1,2,−2, etc.
For the sake of keeping this explanation as short as possible, I am going to skip straight to 2, where we will first find success.
Therefore, 2 is a root. However, it is always important to check to see if a root is in fact a double root (it works twice). Therefore, let's try it one more time.
2 does in fact work twice and is thus a double root. Since we only have three terms remainng, we can convert from synthetic back to an algebraic expression.
f(x)=x2+8x+15
We can then factor.
f(x)=(x+3)(x+5)
Writing our root of 2 as an algebraic expression gives (x−2). Since we have double root, we need two of these. Therfore, our final factored expression is.
f(x)=(x−2)(x−2)(x+3)(x+5)
Write the expression in simpliest form WILL GIIVE BRAINLIEST
3 (2x - 3)
Answer: The answer is 6x–9, please mark me as brainliest and have a wonderful weekend. :D
Step-by-step explanation:
Please please help if possible I love you thank you so much!!!❤️❤️❤️ due really soon
Step-by-step explanation:
There is no question here
Answer: Help with what? You forgot to link your question
Step-by-step explanation:
Form A polynomial whose real zeros and degree are given.
What polynomial has zeros of -5,-1.2,5 and degree of 4?
The polynomial function has zeroes as given by x=0
In general, given zeroes of a polynomial function, a, b, c, and d, we can write the function as the multiplication of the factors
(x-a), (x-b), (x- c), and (x-d) then the degrees are 4
simply:
f(x)=(x-a) (x-b) (x- c) (x-d)
In this case, we can show that each of a, b, c, and d are zeroes of the function:
f(a)=(a-a) (a-b) (a-c) (a-d)
= (0) (a-b) (a-c) (a-d)
=0
f(b)=(b-a) (b-b) (b-c) (b-d)
=(b-a) (0) (b-c) (b-d)
=0
f(c)=(c-a) (c-b) (c-c) (c-d)
=(c-a) (c-b) (0) (c-d)
=0
f(d)=(d-a) (d-b) (d-c) (d-d)
=(d-a) (d-b) (d-c) (0)
=0
since the value of the function at x=a, x=b, c, and d are equal to 0, then the function
f(x)=(x-a) (x-b) (x- c) (x-d) has zeroes at a, b, c and d
with the generalized form, we can substitute for the given zeroes,
x=-5, x=-2,0and 5 where a=-5, b=-2, c=0 and x=5
f(x)=(x-(-5)) (x-(-2)) (x-0) (x-5)
simplifying gives:
f(x)=(x+5) (x+2) x(x-5)
from here, we can put it in standard polynomial form by foiling the right side:
f(x)=x^3+2x^2-25x-50
To double-check the answer, just plug in the given zeroes, and ensure the value of the function at those points is equal to 0.
f (-5) =x^3+2x^2-25x-50
=(-5)^3+2(-5)^2-2(-5)-50
f (-5) =0
f (-2) =(-2)^3+2(-2)^2-2(-2)-50
f (-2) =0
f (0) =0
f (5) =(5)^3+2(5)^2-2(5)-50
=0
Hence, the function has zeroes as given by x=0.
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paper towels are 8$ and the sales tax is 8% what is the total cost of the paper towels?
A)$26
B)$26.50
C)$8.64
D)$2.00
Answer:
The answer is $8.64
You'll multiply 8% by $8 and you'll get 0.64 you'll add that to the total and get the answer
Thomas bought 80 tickets for rides at an amusement park. Each ride cost five tickets, Thomas has been on X right so far. Select all the expressions to show the number of tickets that Thomas has left. A. 80-5x B. 80+5x C. 5(16+x) D.-5x+80 E. 5(16-x)
Answer:
A. 80-5x
Step-by-step explanation:
Let the number of rides be represented by = x
Thomas bought 80 tickets for rides at an amusement park. Each ride cost five tickets, Thomas has been on x right so far.
The number of rides Thomas has been on so far= 5 × x = 5x
The expressions to show the number of tickets that Thomas has left is written as:
80 - 5x
Option A is the correct option.
Answer: clown and watch me and watch all my videos
Step-by-step explanation:
3) Write an equation with a slope of 6 and a y-intercept of 3:
4) Write an equation with a slope of 1.5 and a y-intercept of -5:
given -2 1/3 x -5.15 determine the product.
The resulting product of the expression is 12.017
Product of fractionsFractions are written as a ratio of two integers
Given the following expression
-2 1/3 x -5.15
Convert to improper fraction to have:
-7/3 * -515/100
3605/300
12.017
Hence the resulting product of the expression is 12.017
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Find the missing side of this right triangle
Answer:
x ≈ 14.7
Step-by-step explanation:
use pythagorean therorem
a^2 + b^2 = c^2
c is hypotenuse and we know the hypotenuse is 21
a^2 + b^2 = c^2
x^2 + 15^2 = 21^2
x^2 + 225 = 441
x^2 = 216
x = √216
x ≈ 14.7
a grocery store clerk put only packages of flour tortillas and packages of corn tortillas on a shelf the ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16 which number could be the number of packages of flour tortillas the clerk put on the shelf?
Answer:
1222222222
Step-by-step explanation:
Solve the System of Equations using Substitution or Elimination. State your final
answer as an ordered pair (x,y) *
-3x + 10y = -15
5x - 7y = -4
Answer:
(- 5, - 3 )
Step-by-step explanation:
Given the 2 equations
- 3x + 10y = - 15 → (1)
5x - 7y = - 4 → (2)
Multiplying (1) by 5 and (2) by 3 and adding the result, eliminates the x- term.
- 15x + 50y = - 75 → (3)
15x - 21y = - 12 → (4)
Add (3) and (4) term by term to eliminate x, that is
29y = - 87 ( divide both sides by 29 )
y = - 3
Substitute y = - 3 into either of the 2 equations and solve for x
Substituting into (1)
- 3x + 10(- 3) = - 15
- 3x - 30 = - 15 ( add 30 to both sides )
- 3x = 15 ( divide both sides by - 3 )
x = - 5
solution is (- 5, - 3 )
2) Hector scored 3/5 of the goals on soccer team. If his team scored a total of 35 goals during the season, how many goals did Hector score? Type your answer as a number only. Your answer
Answer:
21
Step-by-step explanation:
1/5 * 35 = 7
7*3 = 21
Someone please help me with this! Pick the correct choice
8-3y=10
solve this equations
Answer:
answer
8-10=3y
-2=3y
y= -2÷3
Step-by-step explanation:
hope it is helpful to you
Can you please awnser this
Answer:62 degrees
Step-by-step explanation: BAC and DAF are equivalent
24 men in a room 1/2 wearing red shirt 1/3 wearing green shirt the rest are wearing blue shirt
Answer:
12 red shirts
8 green shirts
4 blue shirts
Step-by-step explanation:
1/2 of the 24 people are wearing red shirts
Of means multiplication, so...
1/2 * 24 = 24/2 = 12, and do the same for the rest!
Answer:1/2 of 24= 24/2=12
1/3 of 24= 24/3=8
12+8=20
24-20=4
Step-by-step explanation:
I need help with this question can you help me
Answer:
28.26ft
Step-by-step explanation:
A=πr^2
π*3^2=28.27433
28.26
Fill in the blanks so that the equation has infinitely many solutions
5y + 6+ 7y = (blank) (6y + (blank))
solution
5y+7y+6= 12y+6
= 2(6y+3)
Answer:
2(6y + 3)
Step-by-step explanation:
for the equation to have infinitely many solutions, then both sides must be equal.
consider left side
5y + 6 + 7y ← collect like terms
= 12y + 6 ← factor out 2 from each term )
= 2(6y + 3)
then
5y + 6 + 7y = 2(6y + 3) ← has infinitely many solutions
What is the slope of this line? Enter your answer as a whole number or a fraction in simplest form in the box.
Step-by-step explanation:
where is the line? pls share it
Brainliest for whoever gets this right
Answer
14 degrees
Step-by-step explanation:
There is a line whose y intercept is 3 and whose slope is 6. What is its equation in slope-imtercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = 6x + 3
Step-by-step explanation:
Equation of the line
------------------------------------------------------
The equation of the line in slope-intercept form is:
y = mx + b
Being m the slope and b the y-intercept.
Where m is the slope and (h,k) is a point through which the line passes.
We are given the y-intercept as b=3 m=6.
Thus, the equation of the line is:
y = 6x + 3
Each small square on the grid is 1 ft squared.
Which estimate best describes the area of this figure?
A. 25 ft2
B. 35 ft
C. 50 ft2
D. 65 ft2
Which expression can be used to find the product of 320? (3 points)
0 (3 x 2) × (3 x 5)
(3 x 9) * (3 x 5)
(4 x 7) x (2 x 5)
(4 x 8) X (2 x 5)
Will be marked!
Answer:
( 4 x 8) x (2 x 5)
32 x 10
320
1
In a group of tourists 34 are from U.S.A. 44 are from Japan, 64 are from
Germany and 18 are from South Africa. What percentage of the group are
from Japan?
suppose that verania and josimar are roommates that need to complete some household chores. vacuuming and washing dishes need to be done. they know from the last time they did these chores that it takes verania 2 hours to vacuum and 1 hour to wash dishes. it takes josimar 3 hours to vacuum and 2 hours to wash dishes. josimar says it does not matter which task each of them performs because verania is faster at both tasks.
It is wrong. Because Verania has a comparative advantage in washing dishes, she should wash dishes, and Josimar should vacuum.
Having an absolute advantage in both things does not mean that Verania has a Comparative advantage in both as well.
They should find out which activity they both have a comparative advantage in and focus on that. The activity that costs the least opportunity cost is the one they have a comparative advantage.
Verania
Opportunity cost of vacuuming = 2 / 1 = 2 hours of washing dishes
Opportunity cost of washing = 1/2 = 0.5 hours of vacuuming
Josimar
The opportunity cost of vacuuming = 3/2 = 1.5 hours of washing dishes
Opportunity cost of washing = 2/3 = 0.66 hours of vacuuming
Verania has a comparative advantage in washing dishes while Josimar has a comparative advantage in vacuuming.
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Statement: 4x < 0
Which is greater? 1 or x
Answer:
1 is greater than x
Step-by-step explanation:
4x < 0
x<0-4
x< -4
x={ -5,-6,-7,-8,-9,-10,.............}
so {-5,-6,-7,-8,-9,-10,-.............} are lesser than 1
hence 1 >x 0r 1 is greater than x
Solve the system using the method of Your choice.
Answer:
x=3 y=6
Step-by-step explanation:
using elimination
Solve: 8 + b/2 = 14 HELPPPPPPPPPPPPPPPPP
Answer:
b = 12
Step-by-step explanation:
subtract eight from both sides to leave the b variable on the left
b/2 = 14 - 8
b/2 = 6
multiply by 2 on both sides to leave b by itself
b = 6 * 2
b = 12
Answer:
12
Step-by-step explanation:
8 + b/2 = 14
b/2 = 14 -8
= 6
b = 6 x 2
= 12
Therefore b is 12. Hope this helps you and pls mark me as brainliest <3
When is it better to compare data sets using the median instead of the
mean?
Answer:
when the data is skewed
Pls help I’m so bad dependent variables. I’ll give BRAINLIEST answer if you get it right. And pls number it like
1.
2.
3.
Answer:
Develop the concept of flat and solid shapes with your students. This unit has 12 shape activities that include whole group, small group and differentiated math ...
Step-by-step explanation:
I WILL GIVE BRAINILEST
which expression shows a sum of three terms?
3x
3 + x
3 + x + 9
x3
Answer:
the answer would be the third option. its the only thing that has 3 terms
Step-by-step explanation:
3+x+9
Answer:
3+x+9 is the sum of three terms