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
Step2247 [10]
3 years ago
7

The polynomial p(x)=3x^3-20x^2+37x-20 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) =

Mathematics
1 answer:
vesna_86 [32]3 years ago
7 0

Answer:

p(x) = (3x^{2} - 8x + 5)(x - 4)

Step-by-step explanation:

p(x) has degree 3

(x - 4) has degree 1

So p(x) can be rewritten as a polynomial of degree 2 multiplying (x-4)

So

p(x) = (ax^{2} + bx + c)(x - 4)

To find a, b and c, we have to divide p(x) by x - 4.

So

Finding a:

Dividing the first term of p(x) by x - 4.

\frac{3x^{3}}{x - 4} = 3x^{2}

So a = 3.

Now multiplying 3x² by, x - 4, we have:

3x^{2}(x - 4) = 3x^{3} - 12x^{2}

Subtracting p(x) from this:

3x^{3} - 20x^{2} + 37x - 20 - (3x^{3} - 12x^{2}) = 3x^{3} - 20x^{2} + 37x - 20 - 3x^{3} + 12x^{2} = -8x^{2} + 37x - 20

Finding b:

Dividing the first term, after the subtraction, by x - 4.

\frac{-8x^{2}}{x - 4} = -8x

So b = -8.

Multiplying -8x by x - 4, we have:

-8x(x-4) = -8x^{2} + 32x

Then

-8x^{2} + 37x - 20 - (-8x^{2} + 32x) = -8x^{2} + 37x - 20 + 8x^{2} - 32x = 5x - 20

Finding c:

\frac{5x}{x - 4} = 5

So c = 5.

Just to verify if the remainder is 0.

5(x - 4) = 5x - 20

5x - 20 - (5x - 20) = 0

Ok

Then:

p(x) = (ax^{2} + bx + c)(x - 4)

p(x) = (3x^{2} - 8x + 5)(x - 4)

You might be interested in
if Cory is at the elephant and he walks 8 units up and 4 units right, where would he land? What are his new coordinates?
Sati [7]

Answer:

(-2,7) those are the coordinate. in which he will land

4 0
2 years ago
Find the slope of the line graphed beloW.​
sergey [27]

Answer:

1/2

Step-by-step explanation:

u need to use those red dots

with the dot at the bottom you go 1 square to the right

and then you go 2 squares up

and ur answer is 1/2 and you might want to use rise over run = rise/run

7 0
3 years ago
What additional information is needed to prove the triangles are congruent by the SAS Prostulate
VladimirAG [237]
It is that the angle has to be formed by two pairs of congruent/corresponding sides of the triangle
8 0
2 years ago
HELP ASAP!!!! 20PTS
charle [14.2K]

Answer:

m = 36

Step-by-step explanation:

1/3 m+3- 5/6 m=-15

2m+18-5m=-90

-3m+18=-90

-3m=-90-18

-3m=-108

m=36

6 0
2 years ago
Read 2 more answers
Evaluate each numerical expression
ioda

{3}^{4}  - ( - 4)^{2}  =81 - (16) = 65

I hope I helped you^_^

7 0
2 years ago
Read 2 more answers
Other questions:
  • Which of the following is not a zero of f(x) = (x2 - 4x + 4) (x2 + 3x - 10) = 0
    11·1 answer
  • What is the sum of the polynomials?
    5·1 answer
  • Find the perimeter of the trapezoid below.
    12·1 answer
  • A cylinder has a diameter of 6 cm and a height of 14 cm. What is the approximate volume of a cone with the same diameter and hei
    12·1 answer
  • What does 迪兹坚果 mean?​
    5·1 answer
  • 6) There are many cylinders with a height of 4 inches.
    11·1 answer
  • Analyze the diagram below and complete the instructions that follow.
    11·1 answer
  • Help!! I’ve been Stuck on this last problem
    10·1 answer
  • Question 4<br> 1 pts<br> Solve:<br> -(x-8)= -2<br> x = [a]
    13·1 answer
  • Please help me x^2/x^2 times x^2
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!