Give a polynomial of degree 3 that has zeros of 18, 10i, and −10i, and has a value of −3434 when x=1. Write the polynomial in standard form axn+bxn−1+….

The polynomial in standard form is:

The zeros of the polynomial are 18, 10i and -10i.

So, the polynomial is:

Open bracket

Apply difference of two squares

Expand

In complex numbers, i^2 = -1.

So, we have:

Expand

From the question, P(1) = -34.

So, we have:

Divide both sides by -17

Make (a) the subject

Substitute in

Expand

Open bracket

Hence, the polynomial in standard form is:

Read more about polynomials at:

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Given:

Polynomial of degree 3 that has zeros of 18, 10i, and −10i, and has a value of −34 when x=1.

To find:

The polynomial in standard form.

Solution:

If c is a zero of a polynomial then (x-a) is a factor of that polynomial.

18, 10i, and −10i are zeroes, so (x-18), (x-10i) and (x+10i) respectively are the factors of given polynomial.

So, the three degree polynomial is

where, a is a constant.

      ...(i)

The value of P(x) is -34 at x=1.

Divide both sides by 1717.

Put this value in (i).

Therefore, the required polynomial is .

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

soo this can be solve by using the formula:

f = p( 1 + i)^ n

where f is the future profit

p is the initial profit

i is the percent increase

n is the number of years

a . f = 30000 ( 1.05)^n

b. f = 30000 ( 1.05)^15

f = $62,368