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
Nata [24]
3 years ago
9

When a polynomial f(x) is divided by 2x-3,the quotient is x^2-x+2 and the remainder is -1. Find the f(x)​

Mathematics
1 answer:
joja [24]3 years ago
3 0

Answer:

f(x) = 2x³ - 5x² + 7x - 7

Step-by-step explanation:

In the division statement: m ÷ n = q + \frac{r}{n}

  • m is the dividend
  • n is the divisor
  • q is the quotient
  • r is the remainder
  • m = q × n + r

Let us use the fact above to solve the question

∵ f(x) is divided by (2x - 3), the quotient is x² - x + 2 and the remainder is -1

∴ f(x) is the dividend ⇒ m

∴ (2x - 3) is the divisor ⇒ n

∴ (x² - x + 2) is the quotient ⇒ q

∴ -1 is the remainder ⇒ r

→ Use the rule above to find f(x)

∵ f(x) = (x² - x + 2) × (2x - 3) + -1

∴ f(x) = (x² - x + 2)(2x - 3) - 1

→ Multiply the 2 brackets at first

∵ (x² - x + 2)(2x - 3) = x²(2x) + x²(-3) + -x(2x) + -x(-3) + 2(2x) + 2(-3)

∴ (x² - x + 2)(2x - 3) = 2x³ - 3x² - 2x² + 3x + 4x - 6

→ Add the like terms

∴ (x² - x + 2)(2x - 3) = 2x³ + (-3x² - 2x²) + (3x + 4x) - 6

∴ (x² - x + 2)(2x - 3) = 2x³ + (-5x²) + 7x - 6

∴ (x² - x + 2)(2x - 3) = 2x³ - 5x² + 7x - 6

→ Substitute it in f(x)

∴ f(x) = 2x³ - 5x² + 7x - 6 - 1

→ Add the like term

∵ f(x) = 2x³ - 5x² + 7x + (- 6 - 1)

∴ f(x) = 2x³ - 5x² + 7x + (-7)

∴ f(x) = 2x³ - 5x² + 7x - 7

You might be interested in
What is the least common multiple of 2, 3, and 20?
tia_tia [17]

Answer:

60

Step-by-step explanation:

The least common multiple of 2 and 20 is 20.

The only factor that is shared with 20 and 3 is 1. Therefore, the least common multiple will have to be 20*3, which is 60.

<u />

3 0
2 years ago
Read 2 more answers
A floor lamp costs $21 less than a $99 painting. How much does the floor lamp cost?
lesya [120]
99-21=78

Answer:The floor lamp costs $78
6 0
3 years ago
Read 2 more answers
4) What is the present value of $4000 received at the
Bingel [31]

Answer:

$11040

Step-by-step explanation:

first of all the question says that $4000 were earned in a year and asks for what the new vale would be after the next 3 years with a discount rate of 8%.

If 1 year=$4000,then 3 years=$12000

100%-8%=92% (this happens because there is still a remaining amount that still has a cost to it),so 12000*92%=$11040

8 0
3 years ago
Read 2 more answers
At a concert 20% of the people are wearing black dress suits,1/4 are wearing navy,0.35 are wearing brown,and the rest are wearin
yan [13]

Answer:67

Step-by-step explanation: cause tghe number is not a number

5 0
3 years ago
Can <br> a. True <br> b. False results be in a probability distribution
Alexxandr [17]
I think the answers True hope this helps
5 0
3 years ago
Other questions:
  • Use a graphing calculator to solve the equation -2sin(theta)= 1.2 in the interval from 0 to 2pi.
    7·1 answer
  • Whats equivalent to 1/5
    14·1 answer
  • F(x) = {4x² – 1,<br> x = -2<br> x &gt; -2<br> la<br> -x,<br><br> what is f(0)
    12·1 answer
  • I need help with the equation 2/9 = j/18
    10·1 answer
  • Please show all work! Thank you so much
    5·1 answer
  • Someone please help me
    14·1 answer
  • Diring a scuba dive ,lainey descended to apoint 30 feet below the ocean surace.she continued her descent at a rate of 30 feet pe
    12·1 answer
  • -3 13/24 divided by 1 7/8 = ___________?
    11·2 answers
  • 8/15-1/5<br><br> For points or brainliest
    5·2 answers
  • Help with this please!!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!