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just olya [345]
3 years ago
15

This app doesn’t know how to read a picture

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
5 0
It’s the 3rd one hopefully this helps
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1. Make sure your answers and work is SHOWN please and steps are in order.
JulijaS [17]

Been a while since I've done synthetic division.

1a. Let's assume that's supposed to be an equals sign

p(x) = 2x⁴ - 3x³ - 6x² + 5x + 6

possible rational roots have factors of 6 in the numerator and of 2 in the denominator.  We'll only worry about negative numerators.

Factors of six: 1,2,3,6, and we don't forget -1,-2,-3,-6

Factors of 2: 1,2

Possible rational roots:

(dividing by 1:) 1,-1,2,-2,3,-3,6,-6

(dividing by 2:) 1/2, -1/2  (2/2=1 is a duplicate, don't have to repeat it), 3/2, -3/2

Possible rational roots: 1,-1,2,-2,3,-3,6,-6, 1/2, -1/2, 3/2, -3/2

Synthetic division, trying x=1,

   1 | 2  -3  -6  5  6

             2  -1  -7  -2

       2    -1  -7  -2  4

Got a remainder of 4, so 1 isn't a root;

Trying x=-1  

-1 | 2  -3  -6  5  6

         -2   5  1  -6

     2  -5  -1  6  0

Zero remainder, found a root, x=-1.  This division says

(2x⁴ - 3x³ - 6x² + 5x + 6) / (x + 1) = 2x³ - 5x² - x + 6

Same set of rational roots on the cubic, we continue with x=2

2 | 2 -5 -1 6

         4 -2 -6

    2  -1 -3 0

Another zero remainder, x=2 is a root.  We're left with 2x² - x - 3 = 0, which factors as

(2x - 3)(x + 1) = 0

That's a second factor of x+1.  Our final factorization is

2x⁴ - 3x³ - 6x² + 5x + 6 = (x + 1)²(x-2)(2x - 3)

Fourth degree with a positive leading coefficient so goes to +infinity at both ends.  Double zero at x=-1, so it's tangent there, just touching the x axis, then down through x=3/2 and up through x=2.  

I'll leave the actually sketching and the other two polynomials to you -- that took some time.

4 0
3 years ago
Solve the equation x-20.7=9.5 for x
kenny6666 [7]
The answer will come out to 30.2
8 0
2 years ago
Read 2 more answers
Gus makes 48 fluid ounces of spiced cider. If he serves an equal amount to each of 7 people, will each person get more than I cu
Anni [7]

Answer:

Each person get less than 1 cup of cider.

Step-by-step explanation:

1. Calculate the amount of cider served to each person:

Total amount of cider is 48 fluid ounces

Gus serves 7 people

Let Q the amouunt of cider served to each person:

Q=\frac{48}{7}=6.85

Then, each person recived 6.85 fluid ounces of spiced cider.

2. Calculate the number of cups served:

Considering that 1 cup=8 fluid ounces, then:

Q=6.85\frac{1}{8}=0.85

That means that each person recived 0.85 cups of spiced cider.

Each person get less than 1 cup of cider.

4 0
3 years ago
Read 2 more answers
Five less than a number (n) is 28. Which equation shows this relationship?
Tpy6a [65]
The answer is n - 5 = 28
8 0
3 years ago
Read 2 more answers
If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Andrei [34K]
<h3>Answer:  2p + 3q</h3>

Work Shown:

log(200) = log(2^3*5^2)

log(200) = log(2^3) + log(5^2)

log(200) = 3*log(2) + 2*log(5)

log(200) = 3*q + 2*p

log(200) = 2p + 3q

The log rules I used were

log(A*B) = log(A)+log(B)

log(A^B) = B*log(A)

8 0
3 years ago
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