Match each quadratic equation to its factored form.(3 points)x^2−64 x^2−16x+64 x^2+16x+64 x^2+20x+64 x^2−12x−6 responses(x+8)(x+8)(x−16)(x+4)(x+8)(x−8)(x−8)^2(x+16)(x+4)

Answer 1

To match each quadratic equation to its factored form, we will analyze each equation and then identify the correct factorization.

1. Quadratic: \( x^2 - 64 \)

   • This can be factored using the difference of squares: \[ x^2 - 64 = (x - 8)(x + 8) \]

2. Quadratic: \( x^2 - 16x + 64 \)

   • This can be factored as: \[ x^2 - 16x + 64 = (x - 8)(x - 8) = (x - 8)^2 \]

3. Quadratic: \( x^2 + 16x + 64 \)

   • This can be factored as: \[ x^2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)^2 \]

4. Quadratic: \( x^2 + 20x + 64 \)

   • This can be factored as: \[ x^2 + 20x + 64 = (x + 16)(x + 4) \]

5. Quadratic: \( x^2 - 12x - 6 \)

   • This does not factor nicely with integers; we would need to use the quadratic formula to find its roots.

Now, summarizing the matches:

• \( x^2 - 64 \) → \( (x - 8)(x + 8) \)
• \( x^2 - 16x + 64 \) → \( (x - 8)^2 \)
• \( x^2 + 16x + 64 \) → \( (x + 8)^2 \)
• \( x^2 + 20x + 64 \) → \( (x + 16)(x + 4) \)
• \( x^2 - 12x - 6 \) → not factored with integers

Corresponding pairs:

• \( x^2 - 64 \) → \( (x - 8)(x + 8) \)
• \( x^2 - 16x + 64 \) → \( (x - 8)^2 \)
• \( x^2 + 16x + 64 \) → \( (x + 8)^2 \)
• \( x^2 + 20x + 64 \) → \( (x + 16)(x + 4) \)
• \( x^2 - 12x - 6 \) → no simple integer factorization

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