167k views
2 votes
PRE CAL

f(x)=x^3+x^2+4x+4

Solve with Synthetic division and find all zeros of the function

1 Answer

4 votes
The given polynomial is f(x) = x³ + x² + 4x + 4

Use the Remainder Theorem to identify the first zero.
From the Rational Zeros Theorem, possible zeros are +/- 1, +/- 2, +/- 4.
f(1) = 1 + 1 + 4 + 4 = 10 (not a zero).
f(-1) = -1 + 1 - 4 + 4 = 0 (This is a zero)

Therefore (x+1) is a factor of f(x).
Use Synthetic Division.

-1 | 1 1 4 4
-1 0 -4
----------------
1 0 4 0

There is no remainder, therefore
f(x) = (x+1)(x²+4)
Because x² = -4 yields x = 2i, -2i, there are a pair of conjugate complex zeros.

Answer:
All the zeros are -1, 2i, -2i.
User Ed Landau
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories