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
zmey [24]
2 years ago
8

Show that P(x)=x³-6x²+11x-6 is divisible by x-1.​

Mathematics
2 answers:
creativ13 [48]2 years ago
8 0

Hello haohaoxNienie!

\huge \boxed{\mathfrak{Question} \downarrow}

Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

\huge \boxed{\mathfrak{Explanation} \downarrow}

To show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1, we must divide the polynomial by x - 1. If we get the remainder as 0, then we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

So, let's do the division (steps in the attached picture).

__________________

We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

<h3><u>More steps :-</u></h3>

x² - 5x + 6

= <u>(x - 3) (x - 2)</u> [use the splitting the middle term method].

So, the zeroes are,

(x - 3)

x - 3 = 0

<u>x = 3 ⇨ 1</u><u>s</u><u>t</u><u> </u><u>zero.</u>

(x - 2)

x - 2 = 0

<u>x = 2 ⇨ 2nd zero.</u>

Now, use the values of x on the equation. If we get 0 as the solution of the equation then we can prove that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

p(x) = x³ - 6x² + 11x - 6

p(3) = 3³ - 6(3)² + 11 (3) - 6

p(3) = 27 - 54 + 33 - 6

<u>p(3) = 0.</u>

p(x) = x³ - 6x² + 11x - 6

p(2) = 2³ - 6(2)² + 11 (2) - 6

p(2) = 8 - 24 + 22 - 6

<u>p(2) = 0</u>

Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

Hope it'll help you!

ℓu¢αzz ッ

Montano1993 [528]2 years ago
7 0

HERE IS YOUR ANSWER MATE

HOPE ITS HELPFUL

HAVE A GREAT FUTURE

LOVE FROM INDIA

You might be interested in
Help please! &lt;3
lora16 [44]
-x/2 + 4 > = 6
-x/2 > = 6 - 4
-x/2 > = 2...multiply both sides by -2
x < = -4
_________________________________________
x + 3/2 < 7/4
x < 7/4 - 3/2
x < 7/4 - 6/4
x < 1/4
6 0
3 years ago
Javier has been saving for a digital camera. He finds one on sale for $67.50. It usually costs $90.00. What is the percent of th
sergejj [24]

Answer:

B: 25%

Step-by-step explanation:

$90.00 - $67.50 = $22.5

$22.5 / $90 = 0.25 = 25%

Answer:

B: 25%

6 0
3 years ago
A stone dropped from a bridge strikes the water 2.2 s later. How high is the bridge above thewater
vivado [14]
Let the only force acting on the ball is the gravity (free-failing)  and the ball was initially stationary
vo = 0

s = vot + 1/2 gt^2

s = 1/2 x 10 x (2.2) ^2 = 24.2 m 
3 0
3 years ago
Read 2 more answers
The sum of 2x+7 and −x+12 is equal to 14 what is x?
Alekssandra [29.7K]

Answer:-5


Step-by-step explanation:

2x+7-x+12=14

x+19=14

x=-5

                 


4 0
3 years ago
What is the completely factored form of 4x+20
allsm [11]
Hi there!

Since both 4x and 20 can be divisible by 4 and is greatest able to be divisible by 4, we can divide the 4 and put it outside of the parenthesis in order to factor:

4x / 4 = x
20 / 4 = 5

4 (x + 5) 
would be your answer. 

Hope this helps!
3 0
3 years ago
Other questions:
  • Which equation is in point-slope form and is depicted by the line in this graph?
    9·1 answer
  • 4. Which function below represents the arithmetic sequence 3, 7, 11, 15...? (1 point)
    7·2 answers
  • A. How much carpet does Erin need?
    12·1 answer
  • John had $65.00 to spend on packs of paper for his scrapbook project. The packs of paper sell for $1.87 each.
    12·2 answers
  • Three Friends all have ages that are consecutive integers. The sum of their ages is 48. What is the age of the oldest friend?
    8·2 answers
  • 20points please please help!!!!!!
    15·1 answer
  • Please someone help!5m^2 - 26m -24 =0
    12·1 answer
  • Ayaan has 20 stamps more than 3 times the number of stamps Affan has. If both of them together have 140 stamps. How many stamps
    15·1 answer
  • Points C and D represent the location of two parks on a map. Find the distance between the parks if the length of each unit on t
    9·1 answer
  • Factor and write the x-intercepts 6x^2-5x-21 PLEASE HELP I NEED ANSWER
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!