Given that (x - 1) is a factor of x4 + 2x3 - 2x - 1, what are the solutions of x4 + 2x3 - 2x - 1 = 0? A. -2, 0, 1 B. -1, 0, 1 C. -2, 1 D. -1, 1

Step-by-step explanation:

If x-1 is a factor of x⁴ + 2x³ - 2x - 1, then x-1 =0 is  a factor

if x-1 = 0

x = 1

To get other factors we will divide the polynomial by x-1

Find the division in the attachment

x⁴ + 2x³ - 2x - 1,/x-1 = x³ +3x²+ 3x + 1,

let x = -1 be a factor of the resulting expression

f(-1) = (-1)³ +3(-1)²+ 3(-1) + 1

f(-1) = -1 +3(1)-3 + 1

f(-1) =-1+1-3+3

f(-1) = 0

Since f(-1) =0, hence x+1 is a factor of the resulting polynomial'

Dividing x³ +3x²+ 3x + 1, by x+1 to reduce the power of the polynomial

x³ +3x²+ 3x + 1/x+1 = x²+2x+1

Factorizing x²+2x+1

= x²+2x+1

=x²+x+x+1

= x(x+1)+1(x+1)

= (x+1)(x+1)

if the function is equal to zero

x+1 = 0 and x+1 = 0

x = -1 twice

Hence the solutions to the polynomial are 1 and -1(three times)

  21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

  c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.