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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Factor the polynomial function over the complex numbers.

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! Factor the polynomial function over-example-1
User Marc Nuri
by
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1 Answer

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Answer: (x + 1)(x - 2)(x + i√2)(x - i√2)

Explanation:

f(x) = x⁴ - x³ - 2x - 4

possible rational roots: +/- 1, 2, 4

Use Synthetic Division to find two of the roots (so you are left with a quadratic polynomial)

-1 | 1 -1 0 -2 -4

| ↓ -1 2 -2 4

1 -2 2 -4 0 → remainder is 0 so x = -1 is a root

(x + 1) is a factor

Now find another root using the decomposed polynomial:

2 | 1 -2 2 -4

| ↓ 2 0 4

1 0 2 0 →remainder is 0 so x = 2 is a root

(x - 2) is a factor

Now factor the decomposed polynomial:

x² + 0x + 2

= x² - (-2)

=
\sqrt{x^(2)} +/-
√(-2)

= (x + i√2)(x - i√2)


User AJit
by
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