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
100 points, please help? its my last question im stuck on and im almost done! explanations are appreciated too (i wont forget to
lapo4ka [179]
First box’s is angle addition postulate. The the second box is x=15
7 0
3 years ago
Read 2 more answers
Help please. I'll give the Brainliest.
sdas [7]

Answer:

Options 1,2,3 are correct statements

The first values in an ordered pair ( the coordinates) are the domain : ( -3,-2,-1,0,1)

The second values are the range : (-1,1,2,3,4,5)

One input should have only one output for a function.

But -1 input has 2 outputs: -1 and 3.

Thus, it is a relation and not a function.

Hope it helps :)

Mark it Brainliest pls:)

8 0
3 years ago
Read 2 more answers
I need help I hope it uploaded the pic
jenyasd209 [6]
A number that's bigger than 4.3 is the answer :)
8 0
3 years ago
The graph shows the function f(x) = |x – h| + k. What is the value of k? k = –2.5 k = –A. k = –2.5
DedPeter [7]

k is the y-coordinate of the vertex of the function. That vertex is located at (1, -2.5).

The value of k is ...

... A. k = -2.5

5 0
3 years ago
Read 2 more answers
What is the perimeter of triangle ABC<br><br>12 units<br>13units<br>14units<br>18units​
emmainna [20.7K]

Answer:

18

Step-by-step explanation:

The length of  side AC can be found by counting the squares between AC:  8.

The length of side BC can be found using the Pythagorean Theorem.  B is 3 units to the right of C and 4 units above C.  Thus:

|BC| = √(3² + 4²) = √25 = 5.

|AC| has the same length:  5.

Thus, the perimeter of this triangle is 5 + 5 + 8, or 18.

4 0
2 years ago
Read 2 more answers
Other questions:
  • Estimate V17 to the nearest tenth.
    14·1 answer
  • Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to solve for x?
    14·2 answers
  • Each month, Terrance spends $128.00 on his car payment, $63.00 for car insurance, and $45.00 on gas. Round each amount to the ne
    5·1 answer
  • Is 1/8 and 8/8 are equal parts??
    9·2 answers
  • I’ll give you brain list if you solve it
    15·1 answer
  • The measurement is 4 and 6 what is the perimeter.
    9·2 answers
  • Y=1/3mx^3 – (m–1)x^2 + 3(m–2)x +1/3
    13·1 answer
  • 3x + 2 ≤ 14 <br><br>-5 + 2x &gt; 15 * <br><br>-2x + 4 ≥ 18 <br><br>HaLp i don't gets
    15·2 answers
  • Tim's phone service charges $24.25 plus an additional $0.18 for each text message sent per month. If Tim's phone bill was $28.75
    9·1 answer
  • What is the lateral surface area of the square pyramid represented by this net?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!