Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ What is the product of the polynomials below?

[tex]
(5x^2 - x - 3)(2x + 6)
[/tex]

A. [tex]10x^3 + 28x^2 + 12x + 18[/tex]

B. [tex]10x^3 + 28x^2 - 12x - 18[/tex]

C. [tex]10x^3 + 28x^2 + 12x + 3[/tex]

D. [tex]10x^3 + 28x^2 - 12x - 3[/tex]

To find the product of the given polynomials [tex]\((5x^2 - x - 3)(2x + 6)\)[/tex], we will multiply each term in the first polynomial by each term in the second polynomial. Here's how you can do the multiplication step-by-step:

1. Multiply the first term of the first polynomial by each term of the second polynomial:
[tex]\[
5x^2 \times 2x = 10x^3
\][/tex]
[tex]\[
5x^2 \times 6 = 30x^2
\][/tex]

2. Multiply the second term of the first polynomial by each term of the second polynomial:
[tex]\[
(-x) \times 2x = -2x^2
\][/tex]
[tex]\[
(-x) \times 6 = -6x
\][/tex]

3. Multiply the third term of the first polynomial by each term of the second polynomial:
[tex]\[
(-3) \times 2x = -6x
\][/tex]
[tex]\[
(-3) \times 6 = -18
\][/tex]

4. Combine all these results:
- [tex]\(10x^3\)[/tex] (from [tex]\(5x^2 \times 2x\)[/tex])
- [tex]\(30x^2\)[/tex] and [tex]\(-2x^2\)[/tex] add up to [tex]\(28x^2\)[/tex] (from [tex]\(5x^2 \times 6\)[/tex] and [tex]\((-x) \times 2x\)[/tex])
- [tex]\(-6x\)[/tex] and [tex]\(-6x\)[/tex] add up to [tex]\(-12x\)[/tex] (from [tex]\((-x) \times 6\)[/tex] and [tex]\((-3) \times 2x\)[/tex])
- [tex]\(-18\)[/tex] (from [tex]\((-3) \times 6\)[/tex])

So, the product of the polynomials is:
[tex]\[
10x^3 + 28x^2 - 12x - 18
\][/tex]

The correct answer is Option B: [tex]\(10x^3 + 28x^2 - 12x - 18\)[/tex].