Question

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

Answer 1

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

We multiply each term in the first polynomial by each term in the second polynomial:

\[
(5x - 2)(x - 3)
\]

1. Multiply \( 5x \) by \( x \):
\[
5x \cdot x = 5x^2
\]

2. Multiply \( 5x \) by \( -3 \):
\[
5x \cdot -3 = -15x
\]

3. Multiply \( -2 \) by \( x \):
\[
-2 \cdot x = -2x
\]

4. Multiply \( -2 \) by \( -3 \):
\[
-2 \cdot -3 = 6
\]

Now, we sum all these results together:
\[
5x^2 - 15x - 2x + 6
\]

Combine the like terms (\(-15x\) and \(-2x\)):
\[
5x^2 - 17x + 6
\]

Therefore, the product of the polynomials \( (5x - 2) \) and \( (x - 3) \) is:
\[
\boxed{5x^2 - 17x + 6}
\]