Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 8, -14, and 3 + 9i

Step-by-step explanation:

To start you need to find the factorials of 8, -14, and 3 + 9i.

The factorials of these numbers are:

  8:   x - 8 = 0

 -14:  x + 14 = 0

  3 + 9i: x - 3 - 9i = 0 *    

  3 - 9i: x - 3 + 9i = 0 *        

(If you look in the files it shows how I got these numbers)

Next, you need to multiply the factorials together.

(x - 3 - 9i)(x - 3 + 9i) = x^2 - 6x + 90

Take that and multiply by your next factorial:

(x + 14)(x^2 - 6x + 90) = x^3 + 8x^2 + 6x + 1260

Multiply that by your final factorial and you have you final answer!

(x - 8)(x^3 + 8x^2 + 6x + 1260) = x^4 + 58x^2 + 1212x - 10,080

I hoped this helped!

*When you have 3 + 9i or anything along the lines of that then you need to find the inverse of it. You simply you simply change the sign that goes before the i term. Change 3 + 9i to 3 - 9i  

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.