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
Marysya12 [62]
2 years ago
8

Find the value of k such that x-2 is a factor of 3x³-kx²+5x+k​

Mathematics
1 answer:
Nuetrik [128]2 years ago
6 0

Answer:

\displaystyle k = \frac{34}{3}

Step-by-step explanation:

We are given the polynomial:

\displaystyle P(x) = 3x^3 - kx^2 + 5x + k

And we want to determine the value of <em>k</em> such that (<em>x</em> - 2) is a factor of the polynomial.

Recall that the Factor Theorem states that a binomial (<em>x</em> - <em>a</em>) is a factor of a polynomial P(x) if and only if P(a) = 0.

Our binomial factor is (<em>x</em> - 2). Thus, <em>a</em> = 2.

Hence, by the Factor Theorem, P(2) must equal zero.

Find P(2):

\displaystyle \begin{aligned} P(2) &= 3(2)^3 - k(2)^2 + 5(2) + k \\ \\ &= 3(8) - 4k + 10 + k \\ \\ &= 34 - 3k  \end{aligned}

This must equal zero. Hence:

\displaystyle \begin{aligned} 34 - 3k &= 0 \\ \\ -3k &= -34 \\ \\ k = \frac{34}{3}  \end{aligned}

In conclusion, <em>k</em> = 34/3.

You might be interested in
Find the probability of the event. The probability of not choosing a black shirt.
Nata [24]

Answer:

10 of 1

Step-by-step explanation:

just think about it

8 0
3 years ago
What is the solution to the system of equations below?
Ymorist [56]

Answer:

6×+÷3=2+4×=6

3x 8x+6 =8×+y1×-2

6 0
3 years ago
Read 2 more answers
A student packages snack mix at a health food store. She uses 1/3 of her supply of sunflower seeds to make a salted snack mix an
LUCKY_DIMON [66]
10 / (1/3); she has 30 pounds of seeds in her supply.
6 0
3 years ago
Need help asap please no scammers!!!!!!!!!!!!!!!
galina1969 [7]

Answer:

111

Step-by-step explanation:

u got scammed

4 0
3 years ago
What is the q1 of 531 469 573 206 374 421 505 489 702
Galina-37 [17]

Answer: Order the data to find the minimum, maximum, and quartiles.

206, 374, 421, 469, 489, 505, 531, 573, 702.

Step-by-step explanation: I hoped this helped in some way or form.

6 0
2 years ago
Other questions:
  • X + 34 = 60 what does "x" equal??
    11·2 answers
  • 5.
    14·1 answer
  • There is the picture I forgot to add it the first time my apologies
    7·1 answer
  • How many different ways can a family visit Philadelphia, Baltimore, and Washington? 3 6 12
    9·2 answers
  • Draw an area model to represent 40×60
    10·2 answers
  • A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the
    11·2 answers
  • Find the number represented by 2² . 32 . 5.
    11·1 answer
  • The figure is used as part of a visual description of an algebraic statement. Which of the following can be that algebraic state
    7·1 answer
  • Select all the correct answers.
    9·1 answer
  • A circle with a radius of 15 yards contains a sector with an area of 609 yde. Find the measure of
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!