To solve the expression [tex]\((x - 5)\left(6x^2 - 4x + 3\right)\)[/tex], we will use the Distributive Property. The Distributive Property tells us that we need to multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
Let's break it down step-by-step:
1. Distribute [tex]\(x\)[/tex] across [tex]\((6x^2 - 4x + 3)\)[/tex]:
[tex]\[
x \cdot (6x^2 - 4x + 3) = 6x^3 - 4x^2 + 3x
\][/tex]
2. Distribute [tex]\(-5\)[/tex] across [tex]\((6x^2 - 4x + 3)\)[/tex]:
[tex]\[
-5 \cdot (6x^2 - 4x + 3) = -30x^2 + 20x - 15
\][/tex]
3. Combine all the terms from steps 1 and 2:
[tex]\[
(6x^3 - 4x^2 + 3x) + (-30x^2 + 20x - 15)
\][/tex]
4. Combine like terms:
[tex]\[
6x^3 + (-4x^2 - 30x^2) + (3x + 20x) - 15
\][/tex]
Simplify this:
[tex]\[
6x^3 - 34x^2 + 23x - 15
\][/tex]
So, the simplified expression is:
[tex]\[
6x^3 - 34x^2 + 23x - 15
\][/tex]
Therefore, the correct answer is:
c) [tex]\(6x^3 - 34x^2 + 23x - 15\)[/tex]
