Question

Find a polynomial f(x) of degree 4 that has the following zeros.

2 ,0 , -5 , -1
Leave your answer in factored form.

Answer 1

ok lets dissect this problem

Answer 2

first off it says "polynomial of degree 4"

Answer 3

that means that the largest x power is 4

Answer 4

yes

Answer 5

a degree 4 polynomial can be written in the form:

\[f(x) = ax^4 + bx^3 +cx^2+ dx + e\]

Answer 6

the letters a b c d e are simply the place where a number would go

Answer 7

so we know what they mean by degree 4 polynomial... but how can we work backwards from the roots and find what the polynomial is???

Answer 8

well if you remember with degree 2 polynomials we did that trick where we "factored"

Answer 9

with those polynomials we ended up with something like this

Answer 10

and with that example what would the roots be?

Answer 11

you still with me?

Answer 12

yes

Answer 13

In your previous math classes we would factor a degree 2 polynomial and if you remember, this is what we get when we factor a polynomial of degree 2: