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3 years ago

What does factoring a polynomial involve?

Mathematics

1 answer:

White raven [17]3 years ago

6 0

Answer:

ANSWER BELOW↓

Step-by-step explanation:

Factoring a polynomial involves writing it as a product of two or more polynomials. It reverses the process of polynomial multiplication. We have seen several examples of factoring already. However, for this article, you should be especially familiar with taking common factors using the distributive property.

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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by

WARRIOR [948]

Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

$z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1$

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

$z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\$

$z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]$

3 0

3 years ago

A skydiver is falling at approximately 28 feet per second. Find the skydiver's change in altitude

Free_Kalibri [48]

9514 1404 393

Answer:

-140 feet

Step-by-step explanation:

The relation between speed, distance, and time can be written ...

distance = speed × time

distance = (28 ft/s)(5 s) = 140 ft

In 28 seconds, the skydiver changed position by 140 feet. Since the direction is presumed to be down (falling), the change in altitude is -140 feet.

7 0

3 years ago

Combine like terms. x^2y-3xy^2-6x^2y

balu736 [363]

The result after combining like terms is: $-5x^2y-3xy^2$

Step-by-step explanation:

Given expression is:

$x^2y-3xy^2-6x^2y$

The like terms are those terms with whom the variable or product of variables is same.

As in the given expression, first and third, both terms have x^2y so both terms are like terms

Combining like terms, means the indicated operation is performed on them

So,

Combining like terms:

$x^2y-6x^2y-3xy^2\\= -5x^2y-3xy^2$

Hence,

The result after combining like terms is: $-5x^2y-3xy^2$

Keywords: Expressions, polynomials

Learn more about polynomials at:

#LearnwithBrainly

3 0

2 years ago

Determine the relationships between the following lines: *

Dennis_Churaev [7]

9514 1404 393

Answer:

the lines are perpendicular

Step-by-step explanation:

You can tell something by looking at the differences of coordinates:

B-A = (6-2, -11-5) = (4, -16) . . . . . Δy/Δx = -16/4 = -4

D-C = (-1-3, 9-10) = (-4, -1) . . . . . Δy/Δx = -1/-4 = 1/4

The product of the slopes of these lines is (-4)(1/4) = -1, so ...

the lines are perpendicular

4 0

2 years ago

I paid $8.50 each for movie tickets and i spend a total of $144.50. If n, represents how many tickets i bought, write and equati

damaskus [11]

Answer:
$144.50/8.50 = n

Explanation:
The word each indicates this equation will use division. We know the total is 144.50, so that will be the number being divided. 8.50 is the number 144.50 is divided by. The quotient will be represented by the variable, n.

8 0

2 years ago

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