1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
poizon [28]
3 years ago
15

What are the zeros of the polynomial function? f(x)=x^4+2x^3-16x^2-2x+15

Mathematics
2 answers:
Gennadij [26K]3 years ago
7 0
<h3><u>(x + 1)(x - 1)(x + 5)(x - 3) is the fully factored form of the polynomial.</u></h3><h3><u>The zeros are (-1, 0), (1, 0), (-5, 0), and (3, 0).</u></h3>

x^4 + 2x^3 - 16x^2 - 2x + 15

We can use the rational roots theorem to find some of the possible roots, and after finding just one root, we can simplify this polynomial.

List factors of 15:

1, 3, 5, 15.

List factors of 1:

1.

Our possible rational factors are:

+/- 1, +/- 3, +/- 5, +/- 15.

To find factors, we can use the remainder theorem.

Replace all x values with 1.

1^4 + 2(1)^3 - 16(1)^2 - 2(1) + 15 = 0

Because the answer is zero, it means that 1 is a root.

We can divide this polynomial by x - 1 to find a simplified form.

After dividing, our quotient is: x^3 + 3x^2 - 13x - 15

We can continue finding factors by using the rational roots theorem. Once we have only three terms, we can try to factor using the AC method.

Our next possible root is -1.

(-1)^3 + 3(-1)^2 - 13(-1) - 15 = 0

We know that -1 is also a root, and so we can divide the polynomial by x + 1.

After diving we're left with x^2 + 2x - 15.

Now, we can try to factor using the AC method.

List factors of -15.

1 * -15

-1 * 15

3 * -5

-3 * 5 (these digits satisfy the criteria.)

Split the middle term.

x^2 - 3x + 5x - 15

Factor binomials.

x(x - 3) + 5(x - 3)

Rearrange binomials.

(x + 5)(x - 3)

Add in the two factors we already factored out.

(x - 1)(x + 1)(x + 5)(x - 3)

olganol [36]3 years ago
5 0

x^4+2x^3-16x^2-2x+15 =0\\\\x^4+x^3+x^3+x^2-17x^2-17x+15x+15=0\\\\x^3(x+1)+x^2(x+1)-17x(x+1)+15(x+1)=0\\\\(x+1)(x^3+x^2-17x+15)=0\\\\(x+1)(x^3-x^2+2x^2-2x-15x+15)=0\\\\(x+1)(x^2(x-1)+2x(x-1)-15(x-1))=0\\\\(x+1)(x-1)(x^2+2x-15)=0\\\\(x+1)(x-1)(x^2-3x+5x-15)=0\\\\(x+1)(x-1)(x(x-3)+5(x-3))=0\\\\(x+1)(x-1)(x+5)(x-3)=0\\\\x=-1 \vee x=1 \vee x=-5 \vee x=3

You might be interested in
one bag of grapefruit weighs4 pounds. How many pounds of grapefruit are in bags? O 82 pounds Ol pounds o 11 unds O 182 pounds​
Citrus2011 [14]

Answer:

Step-by-step explanation:

The bag weighed 31116 pounds. Explanation: First, we need to get all three of our fractions under a common denominator. To do this, let's first change

8 0
3 years ago
a deck of cards contains red cards number 23 blue cards numbered 1 2 3 4 and green cards numbered one to if a single card is pic
svp [43]

Correct question:

A deck of cards contains RED cards numbered 1,2,3, BLUE cards numbered 1,2,3,4, and GREEN cards numbered 1,2. If a single card is picked at random, what is the probability that the card is BLUE OR has an ODD number?

Answer: 2/13

Step-by-step explanation:

Number of red cards = 3 (1,2,3)

Number of blue cards = 4 (1, 2, 3, 4)

Number of green cards = 2 (1,2)

Total number of cards in a deck = 52

Probability of picking a blue card OR has an odd number

P(picking a blue card ) = required outcome / possible outcome

P( picking a blue card ) = 4/52 = 1/13

P( odd number card ) = 6/52 = 3/26

P(blue and odd) = 2/52 = 1/26

P(picking a blue card or an odd number )

P(picking a blue ) U P(picking an odd number)

P(picking a blue) + (P(picking an odd) - P(picking a blue odd)

1/13 + 3/26 - 1/26= (2 + 3 - 1)/26 = 4/26 = 2/13

6 0
4 years ago
If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?​
Oduvanchick [21]

\large\underline{\sf{Solution-}}

<u>Given:</u>

\rm \longmapsto x = a \sin \alpha  \cos \beta

\rm \longmapsto y = b \sin \alpha  \sin \beta

\rm \longmapsto z = c\cos \alpha

Therefore:

\rm \longmapsto \dfrac{x}{a}  = \sin \alpha  \cos \beta

\rm \longmapsto \dfrac{y}{b}  = \sin \alpha  \sin \beta

\rm \longmapsto \dfrac{z}{c} = \cos \alpha

Now:

\rm =  \dfrac{ {x}^{2} }{ {a}^{2}} +  \dfrac{ {y}^{2} }{ {b}^{2} } +  \dfrac{ {z}^{2} }{ {c}^{2} }

\rm =  { \sin}^{2} \alpha  \cos^{2}  \beta   +  { \sin}^{2} \alpha  \sin^{2} \beta  +  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha  (\cos^{2}  \beta   +  \sin^{2} \beta  )+  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha \cdot1+  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha + { \cos}^{2} \alpha

\rm = 1

<u>Therefore:</u>

\rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} +  \dfrac{ {y}^{2} }{ {b}^{2} } +  \dfrac{ {z}^{2} }{ {c}^{2} }  = 1

5 0
3 years ago
How many gallons of gas did Randy use to drive 189 miles?
Gnesinka [82]

Answer:

i think around 10 gallons. im not sure though,

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Factor the expression completely.<br> 9 - 36x
Nadya [2.5K]

Answer:

9(1-4x)

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • The graph of y = srtqx is translated. The translation is defined by (x + 1, y – 2). Which is the graph of the translated image?
    7·2 answers
  • On a game show, you get to throw a dart at a circle of radius 50 inches. If you miss, you get to throw again until you hit the c
    11·1 answer
  • This beach toy is a square pyramid. It has a height of 4 inches and the base has side lengths of 4 inches. What is the volume?
    13·1 answer
  • Bai is conducting a study on learning. When she manipulates an independent variable, it is possible that some other factor, such
    5·1 answer
  • Simplify the given involving the indicated division. ​
    7·1 answer
  • The diagram shows two parallel lines cut by a transversal.
    14·1 answer
  • PLEASE HELP ME ( MULTIPLE CHOICE) WILL GIVE BRAINLIST
    10·1 answer
  • Latasha earned 18 points on her quiz. If 24 points is equivalent to a score of 100%, which of the following proportions could sh
    12·2 answers
  • 3
    8·1 answer
  • Please help, lots of points and will mark brainliest! :)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!