alleryStart learning →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_
Keep practising Factoring
Browse all Factoring questions for STAAR EOC Algebra I, or explore more Mathematics topics.
Related questions
According to the Sum and Difference of Cubes Pattern, how does a^3+b^3 factor?Factor completely: 36x^2y - 48xy + 16y.Factor completely: 8x^2y - 98y.Factor completely: 6x^2 + 96.What happens when you try to factor a sum of squares like a^2 + b^2?What is the completely factored form of x^4 - y^4?Factor: 100 - h^2.Factor: 121x^2 - 49y^2.