Question

Write a polynomial in standard form that has the following characteristics.

degree 3
leading coefficient of 6
one double root at x=-8
one root at x=7/2

Answer 1

A root of "a" means the polynomial has a factor of (x-a). The factor will be repeated the same number of times the root is repeated. Your polynomial is ...

... f(x) = 6(x +8)²(x-7/2)

... = 3(x² +16x +64)(2x -7) . . . . . multiply out the square

... = 3(2x³ +25x² +16x -448) . . . multiply terms in parentheses

f(x) = 6x³ +75x² +48x -1344