College

We appreciate your visit to Select the correct product x 2 6x 9 3x 1 A 3x 3 19x 2 9x 9 B 3x 3 17x 2 21x 9 C. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Select the correct product.

\[ (x^2+6x+9)(3x-1) \]

A. \[ 3x^3 + 19x^2 + 9x - 9 \]

B. \[ 3x^3 + 17x^2 + 21x - 9 \]

C. \[ 3x^3 - 17x^2 - 21x - 9 \]

D. \[ 3x^3 + 19x^2 + 27x + 9 \]

Answer :

Certainly! Let's find the product of the polynomials [tex]\((x^2 + 6x + 9)\)[/tex] and [tex]\((3x - 1)\)[/tex].

We start by applying the distributive property (also known as the FOIL method when dealing with binomials), where each term in the first polynomial multiplies by each term in the second polynomial.

[tex]\[
(x^2 + 6x + 9)(3x - 1)
\][/tex]

First, distribute [tex]\(3x\)[/tex] to each term in [tex]\((x^2 + 6x + 9)\)[/tex]:

[tex]\[
(3x)\cdot(x^2) = 3x^3
\][/tex]
[tex]\[
(3x)\cdot(6x) = 18x^2
\][/tex]
[tex]\[
(3x)\cdot(9) = 27x
\][/tex]

So, the contributions from [tex]\(3x\)[/tex] are:

[tex]\[
3x^3 + 18x^2 + 27x
\][/tex]

Next, distribute [tex]\(-1\)[/tex] to each term in [tex]\((x^2 + 6x + 9)\)[/tex]:

[tex]\[
(-1)\cdot(x^2) = -x^2
\][/tex]
[tex]\[
(-1)\cdot(6x) = -6x
\][/tex]
[tex]\[
(-1)\cdot(9) = -9
\][/tex]

So, the contributions from [tex]\(-1\)[/tex] are:

[tex]\[
-x^2 - 6x - 9
\][/tex]

Now, add these two sets of terms together:

[tex]\[
3x^3 + 18x^2 + 27x - x^2 - 6x - 9
\][/tex]

Combine like terms:

[tex]\[
3x^3 + (18x^2 - x^2) + (27x - 6x) - 9
\][/tex]
[tex]\[
3x^3 + 17x^2 + 21x - 9
\][/tex]

Thus, the product of [tex]\((x^2 + 6x + 9)\)[/tex] and [tex]\((3x - 1)\)[/tex] is:

[tex]\[
3x^3 + 17x^2 + 21x - 9
\][/tex]

Therefore, the correct answer is:

[tex]\[
\boxed{3x^3 + 17x^2 + 21x - 9}
\][/tex]

Thanks for taking the time to read Select the correct product x 2 6x 9 3x 1 A 3x 3 19x 2 9x 9 B 3x 3 17x 2 21x 9 C. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada