Final answer:
To multiply the polynomials (2r+2)(6r²+3r-1), distribute each term of the first polynomial to each term of the second polynomial, simplify, and combine like terms. The coefficient of the r term in the product is 4.
Step-by-step explanation:
To multiply the polynomials (2r+2)(6r²+3r-1), we use the distributive property. We multiply each term of the first polynomial by each term of the second polynomial. This gives us:
(2r)(6r²) + (2r)(3r) + (2r)(-1) + (2)(6r²) + (2)(3r) + (2)(-1).
Simplifying the expression gives us:
12r³ + 6r² + -2r + 12r² + 6r - 2.
Combining like terms, we get:
12r³ + 18r² + 4r - 2.
The coefficient of the r term in the product is 4.