Final answer:
To multiply (x−4)(x² + 2x−9), use the distributive property to combine like terms, resulting in the expanded expression x³ −2x² −8x + 36, which is the final answer.
Step-by-step explanation:
To multiply the expression (x−4)(x² + 2x−9), we need to apply the distributive property, also known as FOIL (First, Outer, Inner, Last) for polynomials. This involves multiplying each term in the first polynomial by each term in the second polynomial. Below are the steps to complete this multiplication:
- Multiply the First terms: x × x² = x³
- Multiply the Outer terms: x × 2x = 2x²
- Multiply the Inner terms: −4 × x² = −4x²
- Multiply the Last terms: −4 × 2x = −8x
- Multiply −4 by −9 to get +36
Now, combine like terms:
- x³ is the only cubic term.
- 2x² and −4x² combine to become −2x²
- −8x is the only linear term.
- And we have the constant +36.
The fully expanded expression is:
x³ −2x² −8x + 36
This is the final answer, as no further simplification is possible. There is no need to apply the quadratic formula or complete the square, as the product has been simplified to a standard polynomial form.