To find the product of the binomials [tex]\((x^2 - 5)(2x - 1)\)[/tex], we use the distributive property (also known as the FOIL method for binomials). Here's the step-by-step solution:
1. First, distribute each term in the first binomial [tex]\( (x^2 - 5) \)[/tex] to each term in the second binomial [tex]\( (2x - 1) \)[/tex].
2. Multiply [tex]\( x^2 \)[/tex] by each term in [tex]\( 2x - 1 \)[/tex]:
[tex]\[
x^2 \cdot 2x = 2x^3
\][/tex]
[tex]\[
x^2 \cdot (-1) = -x^2
\][/tex]
3. Next, multiply [tex]\(-5\)[/tex] by each term in [tex]\( 2x - 1 \)[/tex]:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot (-1) = 5
\][/tex]
4. Now, add all these results together:
[tex]\[
2x^3 - x^2 - 10x + 5
\][/tex]
So, the product of the binomials [tex]\((x^2 - 5)(2x - 1)\)[/tex] simplifies to:
[tex]\[
2x^3 - x^2 - 10x + 5
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{2 x^3 - x^2 - 10 x + 5}
\][/tex]
