Pergunta
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x^4-8x^2-9
Answer Attempt 2 out of 2
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Factor the expression completely. x^4-8x^2-9 Answer Attempt 2 out of 2 square
Solução
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IdalinaProfissional · Tutor por 6 anos
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To factor the expression x^4 - 8x^2 - 9 completely, we can follow these steps:
1. **Substitute** y = x^2:
x^4 - 8x^2 - 9 \rightarrow y^2 - 8y - 9
2. **Factor** the quadratic expression y^2 - 8y - 9:
We need to find two numbers that multiply to -9 and add up to -8. These numbers are -9 and 1:
y^2 - 8y - 9 = (y - 9)(y + 1)
3. **Substitute back** y = x^2:
(y - 9)(y + 1) \rightarrow (x^2 - 9)(x^2 + 1)
4. **Factor further**:
x^2 - 9 = (x - 3)(x + 3)
x^2 + 1 \text{ cannot be factored further over the real numbers.}
So, the completely factored form of the expression x^4 - 8x^2 - 9 is:
(x - 3)(x + 3)(x^2 + 1)
Thus, the final answer is:
\boxed{(x - 3)(x + 3)(x^2 + 1)}
1. **Substitute** y = x^2:
x^4 - 8x^2 - 9 \rightarrow y^2 - 8y - 9
2. **Factor** the quadratic expression y^2 - 8y - 9:
We need to find two numbers that multiply to -9 and add up to -8. These numbers are -9 and 1:
y^2 - 8y - 9 = (y - 9)(y + 1)
3. **Substitute back** y = x^2:
(y - 9)(y + 1) \rightarrow (x^2 - 9)(x^2 + 1)
4. **Factor further**:
x^2 - 9 = (x - 3)(x + 3)
x^2 + 1 \text{ cannot be factored further over the real numbers.}
So, the completely factored form of the expression x^4 - 8x^2 - 9 is:
(x - 3)(x + 3)(x^2 + 1)
Thus, the final answer is:
\boxed{(x - 3)(x + 3)(x^2 + 1)}
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