Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x + 4)(x – i)(x – 2) f(x) = (x – 3)(x + 4)(x – i)(x – 2) f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2) f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

D is correct

Step-by-step explanation:

We are given roots and leading coefficient of any polynomial.

Roots are -4,i and 2.

All are multiplicity 1.

One root is complex. As we know complex root in conjugate pair.

So, Conjugate of "i" is "-i"

Now, we have four roots with multiplicity 1

Required polynomial:

where, a is leading coefficient

So, a=3

Hence, The required polynomial function is

Step-by-step explanation:

For this case we have the following function:

f (x) = (x + 5) (x + 5) (x + 5) (x + 4) (x - 2) (x - 9)

The leading coefficient is the coefficient that accompanies the variable with the highest degree of the polynomial.

Applying the distributive property, it can be seen that this coefficient is equal to 1.

The roots of the polynomial are given by:

(x + 5) (x + 5) (x + 5) (x + 4) (x - 2) (x - 9) = 0

Solution 1:

x + 5 = 0

x = -5 (multiplicity equal to 3)

Solution 2:

x + 4 = 0

x = -4 (multiplicity equal to 1)

Solution 3:

x-2 = 0

x = 2 (multiplicity equal to 1)

Solution 4:

x-9 = 0

x = 9 (multiplicity equal to 1)

option 3

f (x) = (x + 5) (x + 5) (x + 5) (x + 4) (x - 2) (x - 9)

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the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation:

in the math equation 8 x 7 = 56, the 8 and the 7 are both factors of 56, since in this lesson we will use square tiles to figure out the factors of a whole find as many different arrays as you can, but follow one important rule: all the rows must have the i can make two rows of nine, so 2 and 9 are both factors of 18.

step-by-step explanation: