Factor: x^3 + 64.
A(x-4)(x^2+4x+16)
B(x+4)(x^2+4x+16)
C(x+4)(x^2-4x+16)
D(x+4)(x^2-8x+16)
Answer & Solution
Correct answer: C. (x+4)(x^2-4x+16)
1. Check that the binomial fits the pattern: x cubed is x cubed, and 64 is 4 cubed, so this is a sum of cubes.
2. Write the terms as cubes: a equals x and b equals 4.
3. Apply the sum of cubes pattern: (x + 4)(x squared - 4 times x times 4 plus 4 squared), which simplifies to (x + 4)(x squared - 4x + 16).
4. Check by multiplying: x cubed - 4x squared + 16x + 4x squared - 16x + 64 gives back x cubed + 64.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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