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
Kruka [31]
3 years ago
12

What will be the remainder when 6x ^5+ 4x^4 -27x^

Mathematics
1 answer:
Furkat [3]3 years ago
6 0

Answer:

Remainder = (3145/8)x - 408

Step-by-step explanation:

We want to find the remainder when 6x^(5) + 4x⁴ - 27x³ - 7x² + 27x + 3/2 is divided by (2x² - 3)²

Let's expand (2x² - 3)² to give ;

(2x - 3)(2x - 3) = 4x² - 6x - 6x + 9 = 4x² - 12x + 9

So,we can divide now;

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

First of all, we'll divide the term with the highest power inside the long division symbol by the term with the highest power outside the division symbol. This will give;

3/2x³

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

We now subtract the new multiplied term beneath the original one from the original one to get;

3/2x³

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³+27x +3/2

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³ + (11/2)x²

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

(3/2)x³ + (11/2)x²

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³ + (11/2)x² + (159/8)x

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

(3/2)x³ + (11/2)x² + (159/8)x

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

182x²-(1215/8)x + (3/2)

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³+(11/2)x²+(159/8)x+(91/2)

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

182x²-(1215/8)x + (3/2)

182x²-545x + 819/2

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

182x² - (1215/8)x + (3/2) - 182x² + 545x - 819/2 = (3145/8)x - 408

Remainder = (3145/8)x - 408

You might be interested in
The function f(x)={1/5}^x is translated up 4 units. Which equation represents the translated function
insens350 [35]
f(x+n)\to\text{translation n units left}\\\\f(x-n)\to\text{translation n units right}\\\\f(x)+n\to\text{translation n units up}\\\\f(x)-n\to\text{translation n units down}\\\\\\f(x)=\left(\dfrac{1}{5}\right)^x\to f(x)+4=\left(\dfrac{1}{5}\right)^x+4\\\\Answer:\ g(x)=\left(\dfrac{1}{5}\right)^x+4
3 0
3 years ago
What is the slope of a line that is perpendicular to the line whose equation is 7x−3y=10?
Sonja [21]

Since this equation is already in standard form, there is no need to convert it. Standard form is Ax + By = C. In this equation, 7 = A, 3 = B, and 10 = C. From standard form, Ax + By = C equals negative A over B.

7x + 3y = 10

↓

\displaystyle\ m= \frac{-7}{-3}

Then you'd simplify.

\displaystyle\ m=\frac{7}{3}

The slope cannot be simplified any more, so this would be the final answer.

|

|

<em>- Marlon Nunez</em>

7 0
3 years ago
How do you write 2sin5cos5 as a single trigonomic ratio?
erastova [34]

Answer:

ertyui

Step-by-step explanation:

6 0
2 years ago
Carl throws a single die twice in a row. For the first throw, Carl rolled a 2; for the second throw he rolled a 4. What is the p
siniylev [52]

Answer:

1 over 12.

Step-by-step explanation:

The probability of Carl rolling a 2 is one out of six. The probability of him rolling a 4 is one out of six. but they need to happen one right after the other, so you add them.

6 0
3 years ago
Plz aswer and explain this to me i dont get it
WINSTONCH [101]

Answer: 36

Step-by-step explanation:

1) Find the prime factorization of 12

12=2*2*3

2) Find the prime factorization of 18

18=2*3*3

3) Multiply each factor the greater number of times it occurs in the first two steps above to find the LCM.

LCM=2*2*3*3

4) LCM=36

8 0
3 years ago
Other questions:
  • Find the probability of drawing a black face card on the first draw, replacing it and drawing a 9 card on the second draw
    7·1 answer
  • Use the binomial series to find the maclaurin series for the function. (use (2n)! 2nn! for 1 · 3 · 5 (2n − 1).) f(x) = 1 1 − x5
    13·1 answer
  • What is the s plop of the line passes through the points (-2,15) and (-8,-5) show your work,
    14·1 answer
  • When Tim says that word problems don't use mathematical notation, what does he mean
    7·1 answer
  • Simplify your answer and write as in improper fraction or whole number. <br> 9 divide 7/4
    6·1 answer
  • What is 48 divided by 2 (9+3) =?
    12·1 answer
  • Find the area of the figure. Round to the nearest tenth if necessary. Use 3.14 for .
    6·1 answer
  • A jet travels 584 miles in 4 hours. At this rate how far could the jet fly in 13 hours?what is the rate of speed of the jet
    10·1 answer
  • Sam listed the weighs of his friends. They were 98 , 95 , 64 and 93 pounds. Sam said there were no outliers. Do you agree? Expla
    9·2 answers
  • Plsssssssssssss answer
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!