Question

find the product of polynomials
(3x+5) (2x-7)

Answer 1

To find the product of the polynomials \( (3x + 5)(2x - 7) \), we can use the distributive property (also known as the FOIL method for binomials).

1. **First**: Multiply the first terms:
\[
3x \cdot 2x = 6x^2
\]

2. **Outer**: Multiply the outer terms:
\[
3x \cdot (-7) = -21x
\]

3. **Inner**: Multiply the inner terms:
\[
5 \cdot 2x = 10x
\]

4. **Last**: Multiply the last terms:
\[
5 \cdot (-7) = -35
\]

Now, combine all the results:
\[
6x^2 - 21x + 10x - 35
\]

Next, combine the like terms (-21x and 10x):
\[
6x^2 - 11x - 35
\]

So, the product of the polynomials \( (3x + 5)(2x - 7) \) is:
\[
\boxed{6x^2 - 11x - 35}
\]