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2 years ago

Question 13 of 46 What is the remainder for the synthetic division problem below?

Mathematics

1 answer:

kotegsom [21]2 years ago

7 0

Answer:

Step-by-step explanation:

Let's do this out as best as we can here. Here's the problem:

2 | 3 1 2 -7

___________

The rule is to bring down the first term, whatever it is (ours is a 3), and multiply it by the number "outside" which is a 2. Put that product up under the number next to the 3:

2 | 3 1 2 -7

6

Then add straight down, and multiply that sum by the 2 outside and put that product under the next number (the 2 "inside" the box):

2 | 3 1 2 =7

6 14

3 7

And do the same thing. Add straight down, multiply the sum by 2 and put the product up under the next number, -7, and add again. The final is shown below:

2 | 3 1 2 -7

6 14 32

3 7 16 25

The last number in the very bottom row, the depressed polynomial row, is the remainder. Ours is a 25. This is the super easy way to divide polynomials, as long as our divisor is a linear (first degree) term.

You might be interested in

Researchers at the Centers for Disease Control and Prevention have been studying the decay pattern of a new virus with a decay r

klemol [59]

Answer:

After 7 hours will be 1.95489493x10^12 viruses

Step-by-step explanation:

If the virus spread with 19% per hour after one hour it will increase 57 and continue in the 300+((300*0.19)^7) form, we just need to caculate the form

5 0

3 years ago

What is the solution set of (x-2)(x-3)=3

natali 33 [55]

Answer:

x =(5-√13)/2= 0.697

x =(5+√13)/2= 4.303

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

(x - 2) • (x - 3) - 3 = 0

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring x2-5x+3

The first term is, x2 its coefficient is 1 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3

Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -5 .

-3 + -1 = -4

-1 + -3 = -4

1 + 3 = 4

3 + 1 = 4

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 2 :

x2 - 5x + 3 = 0

Step 3 :

Parabola, Finding the Vertex :

3.1 Find the Vertex of y = x2-5x+3

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000

Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :

y = 1.0 * 2.50 * 2.50 - 5.0 * 2.50 + 3.0

or y = -3.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-5x+3

Axis of Symmetry (dashed) {x}={ 2.50}

Vertex at {x,y} = { 2.50,-3.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 0.70, 0.00}

Root 2 at {x,y} = { 4.30, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-5x+3 = 0 by Completing The Square .

Subtract 3 from both side of the equation :

x2-5x = -3

Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4

Add 25/4 to both sides of the equation :

On the right hand side we have :

-3 + 25/4 or, (-3/1)+(25/4)

The common denominator of the two fractions is 4 Adding (-12/4)+(25/4) gives 13/4

So adding to both sides we finally get :

x2-5x+(25/4) = 13/4

Adding 25/4 has completed the left hand side into a perfect square :

x2-5x+(25/4) =

(x-(5/2)) • (x-(5/2)) =

(x-(5/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-5x+(25/4) = 13/4 and

x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

(x-(5/2))2 = 13/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(5/2))2 is

(x-(5/2))2/2 =

(x-(5/2))1 =

x-(5/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(5/2) = √ 13/4

Add 5/2 to both sides to obtain:

x = 5/2 + √ 13/4

Since a square root has two values, one positive and the other negative

x2 - 5x + 3 = 0

has two solutions:

x = 5/2 + √ 13/4

x = 5/2 - √ 13/4

Note that √ 13/4 can be written as

√ 13 / √ 4 which is √ 13 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-5x+3 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

In our case, A = 1

B = -5

C = 3

Accordingly, B2 - 4AC =

25 - 12 =

Applying the quadratic formula :

5 ± √ 13

x = —————

√ 13 , rounded to 4 decimal digits, is 3.6056

So now we are looking at:

x = ( 5 ± 3.606 ) / 2

Two real solutions:

x =(5+√13)/2= 4.303

or:

x =(5-√13)/2= 0.697

4 0

3 years ago

Read 2 more answers

The jogging track at Francine’s school is 3/4 mile long. Yesterday Francine completed two laps on the track. If she ran 1/3 of t

Alja [10]

Answer:

1/2 of a mile

Step-by-step explanation:

Ok so she ran 1/3 of the distance and you know that the distance is 3/4 of a mile, so you multiply those two together and get 3/12 = 1/4. The total distance is 3/4 so 3/4 - 1/4 = 2/4 = 1/2

7 0

3 years ago

Please help fast PLEASEEEE

AysviL [449]

Answer:

sorry can't help search it up on the internet

Step-by-step explanation:

6 0

3 years ago

HELP 40 POINTS

Tom [10]

Answer: the function g(x) has the smallest minimum y-value.

Explanation:

1) The function f(x) = 3x² + 12x + 16 is a parabola.

The vertex of the parabola is the minimum or maximum on the parabola.

If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.

The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.

When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).

Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.

Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).

Then the minimum value is 4 (when x = - 2).

2) The othe function is g(x)= 2 *sin(x-pi)


The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.

When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2

Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0

3 years ago