Question

Find the product of the polynomials (5x−2)
and (x−3)
.(2 points)
x2 +

x +

Answer 1

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

1. First, distribute \( 5x \) to both terms in the second polynomial:
\[
5x \cdot x = 5x^2
\]
\[
5x \cdot (-3) = -15x
\]

2. Next, distribute \( -2 \) to both terms in the second polynomial:
\[
-2 \cdot x = -2x
\]
\[
-2 \cdot (-3) = 6
\]

3. Now, combine all the terms:
\[
5x^2 - 15x - 2x + 6
\]

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

So, the product of the polynomials \( (5x - 2)(x - 3) \) is:
\[
5x^2 - 17x + 6
\]

In the requested format, we have:
- The coefficient of \( x^2 \) is \( 5 \)
- The coefficient of \( x \) is \( -17 \)
- The constant term is \( 6 \)

Thus, the final answer is:
\[
x^2 + (-17)x + 6
\]