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Find the quadratic polynomial that completes the factorization.
Full solution
Q. Find the quadratic polynomial that completes the factorization.
- Apply sum of cubes formula: To factor , we use the sum of cubes formula, which is .
- Plug in values: Here, is and is . So, we plug and into the formula: .
- Expand and simplify: Now we check if the factorization is correct by expanding to see if we get back.
- Verify factorization: Expanding gives us .
- Verify factorization: Expanding gives us . Simplify the expression by combining like terms: .
- Verify factorization: Expanding gives us . Simplify the expression by combining like terms: . Since we got back the original expression , our factorization is correct.
