Write a polynomial equation of degree 4 that has the following roots:

Question

-1 repeated three times and four

Answer 1

Hi, Chandra!

Since this is a degree 4 polynomial that means when finished your answer will show the highest power of x is 4. So first what you need to do is identify the factors that have these roots: -1,-1,-1,4. Then decide on a variable which I decided on x then just take the opposite of each of the given zeros: (x+1), (x+1) (x+1) and (x-4)

To find the polynomial you then multiply all those factors together: I am choosing to go left to right and beginning to multiply (x+1) by (x+1) by the distribution or FOIL method. However you were taught to multiply polynomials. Another tip is just multiply two polynomials at a time.

(x+1)(x+1)(x+1)(x-4)

x²+x+x+1(x+1)(x-4) Multiplied (x+1)(x+1)

(x²+2x+1)(x+1)(x-4). Combined like terms

(x³+x²+2x²+x+1)(x-4). Multiplied (x²+2x+1)(x+1)

(x³+3x²+x+1)(x-4). Combined like terms

x⁴-4x³+3x³-12x²+x²-4x+x-4 Multiplied (x³+3x²+x+1)(x-4)

x⁴-1x³-11x²-3x-4. Combined like terms

I hope this helps. Have a great day!

Mrs. S

Answer 2

This polynomial f(x) in factored form: f(x) = a(x + 1)³(x - 4), where a ≠ 0 any real number.