Find a polynomial that has the given degree and zeros. Degree 3 with -1, 3, and -5 as zeros x^(3) + {?}x^(2) + {?}x + {?} ​

Question

Find a polynomial that has the given degree and zeros.

Degree 3 with -1, 3, and -5 as zeros


`x^(3) + {?}x^(2) + {?}x + {?}`
​

Answer 1

You can write such a cubic polynomial in terms of its roots using the factor theorem:

(x - (-1)) (x - 3) (x - (-5)) = (x + 1) (x - 3) (x + 5)

Now just expand this:

(x + 1) (x - 3) (x + 5) = x ³ + (1 - 3 + 5) x ² + (-3 + 5 - 15) x - 15

… = x ³ + 3x ² - 13x - 15