Question

Find a polynomial of degree n that has the given zeros. (There are many correct answers.)
zeroes: x=-1,5,7
degree: n=3

Answer 1

We use the fact that if a is a zero then x-a is a factor of the polynomial
so product of all the factors will give us the required polynomial

Answer 2

(x+1)(x-5)(x-7) = 0
is the simplest equation
expand this to get polynomial

Answer 3

so polynomial will be k[(x+1)(x-5)(x-7)]
so now find the product of the three binomials in the bracket n you get yr answer

Answer 4

my problem was the expansion. i knew what you had to do. i just dont know how to expand correctly.

Answer 5

okay ill help you ☺

Answer 6

(x+1)(x-5)(x-7)
first we multiply (x+1)(x-5) = x(x-5) +1(x-5) = x^2 - 5x + x - 5 = x^2 - 4x -5

Answer 7

now we multiply the above result by the third factor
(x^2 - 4x - 5)(x-7) = x^2(x-7) -4x(x-7) -5(x-7)
= x^3 - 7x^2 -4x^2 + 28x -5x + 35
= x^3 - 11x^2 + 23x + 35

Hope it is clear now....☺☻

Answer 8

thank you.

Answer 9

u r welcome..