Answer:
-3x³ + 26x² - 18x + 16
Explanation:
We can multiply factors out to create a singular polynomial.
Multiplication
The first step of simplification is to multiply the factors. To keep our work neat, let's multiply the trinomial (polynomial with 3 three terms) by -x. Then, afterward, multiply the trinomial by 8. Then, we can add these answers together.
We can multiply each term individually and then combine at the end. Let's work from left to right.
- -x * -2x = 2x²
- -x * 2 = -2x
Now, let's combine: -3x³ + 2x² - 2x. Then, let's move on to 8.
Once again we can work from left to right.
- 8 * 3x² = 24x²
- 8 * -2x = -16x
- 8 * 2 = 16
We can combine again: 24x² - 16x + 16. Finally, let's combine all of our answers: -3x³ + 2x² - 2x + 24x² - 16x + 16.
Standard Form
Now that we have one form of the answer, we can further simplify and change to standard form. The last step of simplification is to combine like terms. Like terms are terms with the same variable and exponent.
- -3x³ + 2x² - 2x + 24x² - 16x + 16 = -3x³ + 26x² - 18x + 16
Now, we need to make sure we're in standard form. Standard form is when the terms are written in descending order of degree. This means that the term with the highest exponent should be written first and the constant last. Note that constants are considered to have an exponent of 0. The answer above is actually already in standard form. But, we can check by just making sure the exponents are decreasing from left to right.
The final answer is -3x³ + 26x² - 18x + 16.