Could someone help me please? I am completely lost on how to figure out this problem.Use Synthetic division to show that x is a solution for the third degree polynomial equation and use the result to Factor the Polynomial Completely. List All real solutions of the equation

x^3 - 57x - 56 = 0, x = -1

x = ___ (smallest value)
x = _
x = _____ (largest value)

Answers

Answer 1

Answer: From the factor theorem that says, "The polynomial P(x) has x-r as a factor if and only if r is a root of the equation P(x) = 0." So if you plugged -1 into the x's in the equation and get 0 back then, x+1 is a factor. Let's do it.
$( -1)^(3) -57(-1)-56=-1+57-56=0$
It works. When you plugged -1 into x, you got 0 back and that's what the factor theorem says.
Now let's test it with synthetic division. If we divide x+1 into the original equation and get a remainder of 0, then we should be good. I'll write it up on Paint and upload it.
As you can see, our remainder is 0 and our quotient is $x^(2) -x-56$ . This is the Factor the Polynomial part that you wanted. We can factor this into (x-8)(x+7). So our 3 roots of the equation are (x+1)(x-8)(x+7)
Hope this helps and i'm so sorry for the long reply. I forgot to put 0x^2 when I was doing synthetic division. :/ and also sorry for the unclear paint image. you can zoom in if you want. it's nothing really important it just shows me doing the synthetic division part where i divide x+1 into the original equation.

Answer 2

Answer: x^3 - 57x - 56=0⇒ x(x^2-57)= 56

Verify if x= - 1 is a solution of this equation.
(-1)* [(-1)^2 - 57]=56
(-1)[1 - 57] = 56
(-1)*(-56) = 56

56 =2*28 = (-2)*(-28) = 4*14 = (- 4)*(-14) = 8*7= (-8)*(-7)
x=8 ⇒ 8*(64-57)=56 ok⇒ x=8 is a solution
x= -7 ⇒ (-7)*(49-57)=56 ok ⇒ x= - 7 is a solution

the smallest x= -7
x= - 1
the largest x= 8

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Answers

Answer:

5/12

Step-by-step explanation:

1/4 + 1/6 =

3/12 + 2/12 =

5/12

How much greater is the five in the hundreds place the end of five in the tens place

Answers

it would be 10 times greater im pretty sure.

10 times greater im sure thatll be it

Help to answer 2 & 3 Pablo and Jasmine had just started studying systems of linear equations in algebra. They looked at Pedro's drawing and said, "We could write that as a system of equations." Let t be the price of each taco and d be the price of each drink. - Write an equation that represents the cost of Pablo's order. (6T + 2D = 9) - Write an equation that represents the cost of Jasmine's order. (4T + 2D = 7) 2. What operations with the equations from part (1) match your way of using Pedro's sketch to find the prices t and d? 3. Why do the operations make sense?

Answers

Answer:

Step-by-step explanation:

The equation for Pablo's order is given as 6T+2D=9 or 6T+2D-9=0

While the equation for Jasmine's order is given as 4T+2D=7 or 4T+2D-7=0

Subtracting Jasmine's equation from Pablo's

6T+2D-9-(4T+2D-7)=0

This gives us

6T+2D-9-4T-2D+7=0

The reduces to

2T-2=0

Dividing all through by 2 gives

T-1=0

Therefore

T=1

Substituting the value for T into any of the equations of either Pablo and Jasmine

Using Pablo's

6T+2D=9

6(1)+2D=9

2D=9-6

2D=3

There D= 3/2

1. Your grandmother is in the hospital and is put on a liquid diet. After examining her chart, a mistake is found stating that her weight is 500 kg. What is the equivalent weight in pounds?

Answers

she would weigh 1102.311 pounds

That is 1102.31 pounds

A bag contains 8 blue marbles 5 red marbles and 2 orange marbles , Carolina picks a marble from the bag at random and returns it to the bag and makes a second random selection . What is the probability that two blue marbles were selected

Answers

Initial total number of marbles: 8 + 5 + 2 = 15
Initial number of blue marbles: 8

First pick:
p(blue marble) = 8/15

Since the marble from the first pick is returned to the bag, the bag still contains 8 blue marbles and a total of 15 marbles.

Second pick:
p(blue marble) = 8/15

Overall:
p(blue marble followed by blue marble) =
= p(blue marble) * p(blue marble)
= 8/15 * 8/15
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What is the product? 5/3*10/3a. 23/6
b. -5/7
c. -7/5
d. 5/3

Simplify the expression. (8 + 7a) + 4
a. 12 + 11a
b. 19a
c. 8 + 11a
d. 12 + 7a

Answers

$(5)/(3) * (10)/(3) \n \n (5 * 10)/(3 * 3) \n \n (50)/(3 * 3) \n \n (50)/(9) \n \n 5 (5)/(9) \n \n Answer: \fbox {5 5/9} \ or \ \fbox {5.5556} \n \n ----------- \n \n (8 + 7a) + 4 \n \n 8 + 7a + 4 \n \n 7a + 12 \n \n Answer: \fbox {12 + 7a}$

(5/3)(10/3)

=(5/3)(10/3)

=(5)(10)
--------
(3)(3)

=50/9 (~5.6)

..........

Let's simplify step-by-step.

(8+7a)+4

Combine Like Terms:

=8+7a+4

=(7a)+(8+4)

=7a+12

Answer:

=7a+12 (d.)

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