Question

Please help for brainliest!!:)

Answer 1

9514 1404 393

Answer:

  (c)  P(x) = x^4 +3x^3 -10x^2 -30x

Step-by-step explanation:

If the polynomial has integer coefficients, its complex or radical roots come in conjugate pairs. That is, -√10 is also a root. The four roots mean the polynomial has degree 4. That eliminates all but answer choice C.

Each root 'a' gives rise to a factor (x -a), so the factored polynomial is ...

  P(x) = (x -0)(x -(-3))(x -√10)(x -(-√10))

  P(x) = x(x +3)(x² -10) = x(x³ +3x² -10x -10)

  P(x) = x^4 +3x^3 -10x^2 -10x