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
pochemuha
3 years ago
13

The polynomial p(x)=x^3+7x^2-36p(x)=x 3 +7x 2 −36p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 7, x, square

d, minus, 36 has a known factor of (x+3)(x+3)left parenthesis, x, plus, 3, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p(x)=

Mathematics
2 answers:
Iteru [2.4K]3 years ago
8 0

Answer:

(x-2)(x+3)(x+6)

Step-by-step explanation:

Given the polynomial function p(x)=x^3+7x^2-36

We are to write it as a product of its linear factor

Assuming the value of x that will make the polynomial p(x) to be zero

Let x = 2

P(2) = 2³+7(2)²-36

P(2) = 8+7(4)-36

P(2) = 8+28-36

P(2) = 0

Since p(2) = 0 hence x-2 is one of the linear factors

Also assume x = -3

P(-3) = (-3)³+7(-3)²-36

P(-3) = -27+7(9)-36

P(-3) = -27+63-36

P(-3) = 36-36

P(-3) = 0

Since p(-3) = 0, hence x+3 is also a factor

The two linear pair are (x-2)(x+3)

(x-2)(x+3) = x²+3x-2x-6

(x-2)(x+3) = x²+x-6

To get the third linear function, we will divide x^3+7x^2-36 by x²+x-6 as shown in the attachment.

x^3+7x^2-36/x²+x-6 = x+6

Hence the third linear factor is x+6

x^3+7x^2-36 = (x-2)(x+3)(x+6)

spin [16.1K]3 years ago
8 0

Answer:

x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)

Step-by-step explanation:

Here we want to rewrite the polynomial

P(x) = x^3 + 7x^2 - 36

As a product of linear factors given that we have one of the roots already as (x + 3)

What we shall do here is to divide the polynomial by x + 3

Please check attachment for long polynomial division

From the division, the other factor is x^2 + 4x -12

So we can rewrite the polynomial as;

x^3 + 7x^2 -36 = (x + 3)(x^2 + 4x -12)

So let’s now write x^2 + 4x -12 as a product of its linear factors

x^2 + 4x -12 = x^2 + 6x -2x -12

= x(x + 6)-2(x + 6)

so we have;

(x -2)(x + 6)

Therefore;

x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)

You might be interested in
Help I don’t understand this
bogdanovich [222]

Answer:

tan 33° = 25/x

Step-by-step explanation:

hope it helps

5 0
3 years ago
Im getting my grade up soo help
Ket [755]
Where is pic…………………,,,,,
4 0
2 years ago
Read 2 more answers
Divide 28 bottles of water into two groups so the ratio is 3 to 4. Be sure to show your work.
tatyana61 [14]

Answer:

12:16

Step-by-step explanation:

28 split into two groups could be 12 : 16. To check the work, see if 3/4 is equal to 12/16. It is, so this is the accurate ratio, as 12 + 16 = 28 and 12/16 = 3:4.

4 0
2 years ago
Please solve this...I can;t do it do it
yanalaym [24]

Answer:

Area = 867 meters

Step-by-step explanation:

You have a rectangle. This means opposite sides are equal. If you set these expressions equal to each other, you will get two equations with two unknowns, x and y. Next, solve the system of equations to find x and y. Then, use the values to find the length and width of the rectangle. Last, multiply length × width to find the area.

8 0
2 years ago
Whats 1x600 plssssssssssssssssssssssssssssssssssss
Andre45 [30]

Answer:

600

Step-by-step explanation:

anything times 1 is itself

5 0
2 years ago
Read 2 more answers
Other questions:
  • The chess club members bought 6 tickets to a tournament for $15.How much would they have paid if all 9 members wanted to go? Sho
    8·2 answers
  • What is the total cost for an item that costs 26.50 and has a sales tax rate of 6%
    13·1 answer
  • A water bottle holds Fraction 5 over 8 liter of water when it is Fraction 3 over 4 full. Which statement best describes the quot
    11·1 answer
  • Can someone help me find x
    12·1 answer
  • Using similar triangles if KLM~ PQR with a scale factor of 3:5, find the perimeter of PQR (With work please)
    8·2 answers
  • Why is6-8 greater than 5-8 but less than 7-8?
    12·1 answer
  • Determine the radius of a cone that has a volume of 230 ft' and a height of 15 ft.
    5·1 answer
  • Anyone 100% know dis answer
    8·1 answer
  • A train leaves the station at time = 0. Traveling at a constant speed, the train travels 330 kilometers in 3 hours. Answers part
    15·1 answer
  • Use the discriminant to determine the number of real solutions to the quadratic equation.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!