Final answer:
The product of (x - 2) and (x² – 3x + 8) is x³ - 5x² + 14x - 16, which is found by distributing each term in the first polynomial across each term in the second polynomial and combining like terms.
Step-by-step explanation:
To express the product of (x - 2) and (x² – 3x + 8) in standard form, we use the distributive property to multiply each term in the first polynomial by each term in the second polynomial:
- Multiply x by x² to get
- Multiply x by -3x to get -3x²
- Multiply x by 8 to get 8x
- Multiply -2 by x² to get -2x²
- Multiply -2 by -3x to get 6x
- Multiply -2 by 8 to get -16
Combine like terms:
- stays the same.
- Add -3x² and -2x² together to get -5x²
- Add 8x and 6x to get 14x
- <-16> stays the same.
The product in standard form is x³ - 5x² + 14x - 16, which corresponds to answer choice (B).