College

What is the product?

\[ (7x^2)(2x^3 + 5)(x^2 - 4x - 9) \]

A. \[ 14x^5 - x^4 - 46x^3 - 58x^2 - 20x - 45 \]

B. \[ 14x^6 - 56x^5 - 91x^4 - 140x^3 - 315x^2 \]

C. \[ 14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2 \]

D. \[ 14x^{12} - 182x^6 + 35x^4 - 455x^2 \]

Answer :

To solve the expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], follow these steps to find the product:

1. Distribute the First Term:
Start by distributing [tex]\(7x^2\)[/tex] to each term in the expression [tex]\(2x^3 + 5\)[/tex].

[tex]\[
(7x^2)(2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5 = 14x^5 + 35x^2
\][/tex]

2. Multiply the Result by the Third Polynomial:
Now, take the result from step 1, [tex]\(14x^5 + 35x^2\)[/tex], and distribute it to each term in [tex]\(x^2 - 4x - 9\)[/tex].

[tex]\[
(14x^5 + 35x^2)(x^2 - 4x - 9)
\][/tex]

- First, distribute [tex]\(14x^5\)[/tex]:

[tex]\[
14x^5 \cdot x^2 = 14x^7
\][/tex]

[tex]\[
14x^5 \cdot (-4x) = -56x^6
\][/tex]

[tex]\[
14x^5 \cdot (-9) = -126x^5
\][/tex]

- Next, distribute [tex]\(35x^2\)[/tex]:

[tex]\[
35x^2 \cdot x^2 = 35x^4
\][/tex]

[tex]\[
35x^2 \cdot (-4x) = -140x^3
\][/tex]

[tex]\[
35x^2 \cdot (-9) = -315x^2
\][/tex]

3. Combine All Terms:

Combine all the terms you calculated above:

[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]

This results in the final product of the expression. The polynomial is:

[tex]\[
\boxed{14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2}
\][/tex]

Other Questions