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lakkis [162]
3 years ago
7

Multiply.

Mathematics
1 answer:
Ilya [14]3 years ago
3 0

Answer:

Use synthetic division to determine whether x – 4 is a factor of:

–2x5 + 6x4 + 10x3 – 6x2 – 9x + 4

For x – 4 to be a factor, you must have x = 4 as a zero. Using this information, I'll do the synthetic division with x = 4 as the test zero on the left:

completed division

Since the remainder is zero, then x = 4 is indeed a zero of –2x5 + 6x4 + 10x3 – 6x2 – 9x + 4, so:

Yes, x – 4 is a factor of –2x5 + 6x4 + 10x3 – 6x2 – 9x + 4

Find all the factors of 15x4 + x3 – 52x2 + 20x + 16 by using synthetic division.

Remember that, if x = a is a zero, then x – a is a factor. So use the Rational Roots Test (and maybe a quick graph) to find a good value to test for a zero (x-intercept). I'll try x = 1:

completed division

This division gives a zero remainder, so x = 1 must be a zero, which means that  x – 1 is a factor. Since I divided a linear factor (namely, x – 1) out of the original polynomial, then my result has to be a cubic: 15x3 + 16x2 – 36x – 16. So I need to find another zero before I can apply the Quadratic Formula. I'll try x = –2:

completed division

Since I got a zero remainder, then x = –2 is a zero, so x + 2 is a factor. Plus, I'm now down to a quadratic, 15x2 – 14x – 8, which happens to factor as:

(3x – 4)(5x + 2)

Then the fully-factored form of the original polynomial is:

15x4 + x3 – 52x2 + 20x + 16

= (x – 1)(x + 2)(3x – 4)(5x + 2)

Given that  x = -3 + sqrt(11)   is a zero of x4 + 6x3 – 7x2 – 30x + 10, fully solve the

equation x4 + 6x3 – 7x2 – 30x + 10 = 0.

Since they have given me one of the zeroes, I'll use synthetic division to divide it out:

completed division

(You will probably want to use scratch paper for the computations required when manipulating the radical root.) Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

Since you only get these square-root answers by using the Quadratic Formula, and since the square-root part of the Formula is preceded by a "plus-minus" sign, then these square-root answers must always come in pairs. Thus, if x = -3 + sqrt(11) is a root, then so also must x = -3 - sqrt(11) be a root. So my next step is to divide by x = -3 - sqrt(11):

completed division

I had started with a fourth-power polynomial. After the first division, I was left with a cubic (with very nasty coefficients!). After the second division, I'm now down to a quadratic (x2 + 0x – 5, or just x2 – 5), which I know how to solve:

x = +/- sqrt(5)

Then the full solution is:

x = -3 +/- sqrt(11), +/- sqrt(5)

If you have studied complex numbers, then you may see a problem of the following type.

Given that 2 – i is a zero of x5 – 6x4 + 11x3 – x2 – 14x + 5, fully solve the

equation  x5 – 6x4 + 11x3 – x2 – 14x + 5 = 0.

They have given us a zero, so I'll use synthetic division and divide out 2 – i:

completed division

(You will probably want to use scratch paper for the computations required when doing complex division.)

Recall that, to arrive at a zero of 2 – i, they must have used the Quadratic Formula, which always spits out complex answers in pairs. That is, you get the imaginary part (the part with the "i") from having a negative inside the "plus or minus square-root of" part of the Formula. This means that, since 2 – i is a zero, then 2 + i must also be a zero.  So I'll divide by 2 + i:

completed division

This leaves me with a cubic, so I'll need to find another zero on my own. (That is, I can't apply the Quadratic Formula yet.) I can use the Rational Roots Test to help find potential zeroes, and a quick graph of x3 – 2x2 – 2x + 1 can help. I will try x = –1:

completed division

Now I'm down to a quadratic (x2 – 3x + 1, which happens not to factor), so I'll apply the Quadratic Formula to get:

x = (3 +/- sqrt(5))/2

Then all the zeroes of x5 – 6x4 + 11x3 – x2 – 14x + 5 are given by:

x = 2 - i, 2 + i, (3 - sqrt(5))/2, (3 + sqrt(5))/2, -1

Step-by-step explanation:

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BRO SOMEONE PLEASE HELP ME OUT BRO I FR NEED SOME HELP. HOW DO YOU DO THIS
Finger [1]

Answer:

there you go bro. 168 degrees   for each angle

Step-by-step explanation:

To calculate the central angle visualize a circle in the center of the polygon. A circle has 360 degrees. Divide 360 by the number of sides and that will tell you the central angle size. So 360 divided by 30 equals 18 degrees.

To find the base angle use this formula

180(n-2)/n where n is the number of sides of a regular polygon.

When you plug in 30 for n

4 0
3 years ago
An object is thrown upward from the top of a 192 ft building with an initial velocity of 64 feet
Airida [17]

Answer:

t=6

Step-by-step explanation:

ground height = 0

(are you sure your formula is correct? isn't it - 16t²?)

if h=16t² +64t+192 is true then

16t² +64t+192 = 0

t² + 4t + 12 = 0

t = (-4 ± √(4² - 4*12)) / 2*1 = (-4 ± √-32) / 2 = -2 ± 2√-2

There is no solution of t

if it is h= - 16t² +64t+192

0 =- 16t² + 64t + 192

t² - 4t - 12 = 0

(t + 2) (t -6) = 0

t should be positive

t = 6 sec

7 0
3 years ago
A large high school offers AP Statistics and AP Calculus Among the seniors in this school 65% take AP Statistics, 45% take AP Ca
Igoryamba

Answer:

0.8

Step-by-step explanation:

P(AP statistics) = 65%

P(AP Calculus) = 45%

P(AP statistics n AP Calculus) = 30%

Probability of AP statistics or AP Calculus but not both :

Probability of event A or B :

P(AUB) = p(A) + p(B) - p(AnB)

P(AP statistics U AP Calculus) = P(AP statistics) + P(AP Calculus) - P(AP statistics n AP Calculus)

= 0.65 + 0.45 - 0.30

= 0.8

= 80%

4 0
2 years ago
Simplify the expression.
butalik [34]
Hey there! :D

That's like saying:

-2*-2*-2

-2*-2=4

4*-2= 8

"D" -8 <== the answer 

I hope this helps!
~kaikers
8 0
3 years ago
Read 2 more answers
3. A rectangular prism has dimensions of ½ 2, and 7/2 in.
sp2606 [1]

Answer:

answer c is 28 cubes

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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