Multiply the polynomials (2r−5)(r+4).(2 points)

Question

__r^2+__r+__

Answer 1

To multiply the polynomials \( (2r - 5)(r + 4) \), we can apply the distributive property (also known as the FOIL method for binomials).

1. Multiply the first terms: \( 2r \cdot r = 2r^2 \)
2. Multiply the outer terms: \( 2r \cdot 4 = 8r \)
3. Multiply the inner terms: \( -5 \cdot r = -5r \)
4. Multiply the last terms: \( -5 \cdot 4 = -20 \)

Now, combine all these results:

\[ 2r^2 + 8r - 5r - 20 \]

Combine like terms:

\[ 2r^2 + (8r - 5r) - 20 = 2r^2 + 3r - 20 \]

The final result is:

\[ 2r^2 + 3r - 20 \]

So, filling in the blanks:

__r^2 + __r + __

would be:

2r^2 + 3r - 20.