Find a polynomial of degree 4 and the zeros are -2, 4, 4, 8

Required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is

Need to determine a polynomial of degree 4 and the zeros are -2, 4 , 4 and 8

Let the required polynomial be represented by f(x)

The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial.

If the polynomial p(x) is divided by cx−d and the remainder, given by p(d/c), is equal to zero, then cx−d is a factor of p(x).

-2 is zero of a polynomial means when x = -2, f(-2) = 0, so from factor theorem we can say that  

=> x = -2 that is x + 2 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

8 is zero of a polynomial means when x = 8, f(8) = 0 , so from factor theorem we can say that  

=> x = 8 that is x -8 = 0 is factor of polynomial f(x)

So now we have four factors of polynomial f(x) that are (x + 2), (x -4) , (x -4) and (x – 8)

And as given that degree of polynomial f(x) is 4  

Now f(x) is equal to product of factors

Hence required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is

answer: i literally just answered this question but they want me to do it again

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.

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.