Question

Multiply the polynominal expression (r - 1)(r^2 - 2r + 3)
? r^3 + ? R^2 + ? r + ? (Make it fit the boxes)

Answer 1

To multiply the polynomial expressions \((r - 1)(r^2 - 2r + 3)\), we can use the distributive property.

Let's distribute each term in the first polynomial to each term in the second polynomial:

\[
(r - 1)(r^2 - 2r + 3) = r(r^2 - 2r + 3) - 1(r^2 - 2r + 3)
\]

Now, calculating each part:

1. \(r \cdot (r^2 - 2r + 3) = r^3 - 2r^2 + 3r\)
2. \(-1 \cdot (r^2 - 2r + 3) = -r^2 + 2r - 3\)

Now, combine these results:

\[
r^3 - 2r^2 + 3r - r^2 + 2r - 3
\]

Next, combine like terms:

- The \(r^3\) term: \(r^3\)
- The \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\)
- The \(r\) terms: \(3r + 2r = 5r\)
- The constant term: \(-3\)

Putting it all together, we get:

\[
r^3 - 3r^2 + 5r - 3
\]

So, the polynomial expression fits the format as follows:

\( ? r^3 + ? r^2 + ? r + ? \)

Filling in with the coefficients from our result we have:

\[
1 r^3 + (-3) r^2 + 5 r + (-3)
\]

Thus, the answer is:

1, -3, 5, -3.