I NEED HELP WILL GIVE BRAINLIEST. PLZZZZ

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)

Answer:

each child get 4

Step-by-step explanation:

Answer:

4 marbles

Picture:

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if this trapezoid is to scale, then the scale factor between the shortest and longest side is 1.5

so, that means that 1.5(2x+6) = 4x+2

so, your equation becomes 3x+9 = 4x+2

if you subtract 2 from each side, you get 3x+7 = 4x

meaning that x = 7

i hope this helps, and i'm sorry if it's wrong!! :)

Answer: Murder is a sin

Step-by-step explanation:

The function f(x) = x^4 + 4/x^2 + 1 is an even function

The equation of the function is given as

f(x) = x^4 + 4/x^2 + 1

Calculate f(-x)

So, we have

f(-x) = (-x)^4 + 4/(-x)^2 + 1

Evaluate the exponents

f(-x) = x^4 + 4/x^2 + 1

Calculate -f(x)

So, we have

-f(x) = -[x^4 + 4/x^2 + 1]

Evaluate the product

-f(x) = - x^4 + 4/x^2 + 1

From the above computations, we have

f(x) = f(-x)

This represents an even function

Hence, the function f(x) = x^4 + 4/x^2 + 1 is an even function

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Answer:

This answer is D

Step-by-step explanation:

Answer:

11

or

2(5)+2-3

Step-by-step explanation:

if a = 5 and b=2,

you add it into the expression.

2a + b -3 --> 2(5) + 2 - 3

all you have to do is replace the letters with the (given) numbers.

then, solve.

2(5) = 10

2-3= 1

10+1 =11

the answer is 11.

:)

The Value for the expression 2a + b -3 is 9.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Expression: 2a+ b -3

Now, for a=5 and b=2 thee expression gives

= 2a + b -3

= 2(5) + 2 -3

= 10 +2 - 3

= 12 - 3

= 9

Hence, the Expression valued 9.

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Point P=(-3,1). The point P is rotated 270°. Reflected across y=x. The given image is obtained by rotating a preimage by 270 degrees clockwise and using its coordinates point P"=(3,1).

Given that,

Point P=(-3,1)

The point P is rotated 270°.

Reflected across y=x.

The reflection of (x, y) across the line y = x results in (y, x)

Across the line y = x, P(-3, 1) is reflected (1, -3)

The given image is obtained by rotating a preimage by 270 degrees clockwise and using its coordinates (x, y) is (-y, x)

The given image is produced by rotating the preimage, P, by 270 degrees clockwise. Its coordinates are P = (1, -3) is (3, 1)

Therefore, point  P"=(3,1)

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Answer:

-x^2

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

48 + 22 = 70

70 - 23 = 47

Hope this helped! Let me know if you need a better explanation!

Answer:

-2/3 is the negative inverse of 3/2

Answer:

a. 2w + 2(w+4) = 60

Answer:

the answers a

Step-by-step explanation: the width is 10 and the length is 20

Answer:

slope

Step-by-step explanation:

Answer:

could you get a better picture of it so I could answer or for you?

Answer:

C. 73.5lbs

Step-by-step explanation:

[tex]\frac{5}{30} =\frac{x}{90}[/tex]

Match the denominators:

[tex]\frac{5}{30} *\frac{3}{3}= \frac{15}{90}[/tex]

x = 15

Check your work:

[tex]\frac{15}{90} \div \frac{3}{3} = \frac{5}{30}[/tex]

We know that x = 15

Answer:

7 divided by 1/3 is 21

Step-by-step explanation:

The answer would A! :3

Answer:

3

Step-by-step explanation:

3/10 is 1/3 of 9/10

Answer: 2.7?

Step-by-step explanation:

There are 600 pages in the book.

In this question, we have been given a situation where your Language Arts teacher expects you to read an entire book over the 3 day weekend.

On Tuesday you are on page 60 and are 1/5 of the way done.

We have been given a fraction 1/5.

We need to find the number of pages in the book.

Let 'n' be the number of pages in the book.

60 = 1/5 × n

n = 5 × 60

n = 300

Therefore, there are 600 pages in the book.

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Answer:

Hey give it a try but my answer is 1.5 miles

Step-by-step explanation:

Answer:

I believe it is B.

Step-by-step explanation:

Hope this helps

Answer:

The unit rate = 2 dollars / per pineapple

Point A(7, 14) indicates that the value of 14 pineapples is 7 dollars.

Step-by-step explanation:

The unit rate represents the slope of the line.

It means the slope is often termed as a ratio, which could be expressed as a unit rate found at the point on the graph with the given ordered pairs.

Let us take two points that lie on the graph to determine the unit rate (or slope)

unit rate = slope = y₂-y₁ /  x₂-x₁

                            = 4-2 / 2-1

                            = 2/1

                             = 2

Thus, the unit rate = 2 dollars / per pineapple

The location of point A is (7, 14)

i.e. A(7, 14)

Answer:

D

Step-by-step explanation:

15 - 2.5x = 40 ( isolate the term in x by subtracting 15 from both sides )

- 2.5x = 40 - 15 = 25 ← Step 1

divide both sides by - 2.5

x = 25 ÷ - 2.5 ← Step 2

x = - 10

In the given figure , two sides of the triangle are equal , so it is isosceles triangle . So , as we know that in an isosceles triangle equal side's opposite answers are also equal . Now ,

=> x = 75°

Hence , x = 75°

Using the same property which we used in the above problem ,

• x = x

Now using angle sum property of triangle ,

=> x + x + 40° = 180°

=> 2x + 40° = 180°

=> 2x = 180° - 40°

=> 2x = 140°

=> x = 140° / 2

=> x = 70°

Hence , x = 70° .

Answer:

The ans to the first question would be 75, Coz....

It's an Isosclese triangle, as both sides are equal [The two lines on the triangle indicate that its equal]

So,the angle given is 75 degrees, the other angle would be 75 degrees too.

For the second question-

The same rule applies here, the triangle shown is an isosclese triangle,so the angle x & the angle opposite to x should be equal [The angle opposite or next to angle x is blank, so lets just call it y]

The equation of a triangle goes-

The angles of a triangle add upto 180

So 40+x+y=180

180-40 will give the sum of both angle x & y

180-40=140 [Now we know that x+y=140, we also know that both angles have the same value, so basically they're equal]

this means that we can divide 140 equally into two parts to disturbute the value to both x & y

140/2=70 degrees

So, the ans of x=70 [y is also 70, but the question doesnt  ask for it]

9514 1404 393

Answer:

  18 cm

Step-by-step explanation:

Consider right triangle PCA.

The length PC is the hypotenuse of that triangle. It is also the radius of the circle: 15 cm.

The length AC is AB -CB = (27 -15) cm = 12 cm.

The length AP can be found from the Pythagorean theorem:

  AP² +AC² = PC²

  AP² = PC² -AC² = (15 cm)² -(12 cm)² = (225 -144) cm² = 81 cm²

  AP = √(81 cm²) = 9 cm

Since A is the midpoint of PQ, the length of PQ is double the length of AP:

  PQ = 2·AP = 2·9 cm

  PQ = 18 cm

Answer:

(A) = (3). (B) = (7). (C) = (6)