Question

Multiply to simplify the polynomial expression (2x−3)(x2−4x+5

Answer 1

To simplify the polynomial expression \((2x - 3)(x^2 - 4x + 5)\), we will use the distributive property (also known as the FOIL method for binomials).

Let's multiply each term in the first polynomial by each term in the second polynomial:

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

Now, calculating each of these:

1. \(2x \cdot x^2 = 2x^3\)
2. \(2x \cdot (-4x) = -8x^2\)
3. \(2x \cdot 5 = 10x\)
4. \(-3 \cdot x^2 = -3x^2\)
5. \(-3 \cdot (-4x) = 12x\)
6. \(-3 \cdot 5 = -15\)

Now we combine all of these terms:

\[
2x^3 - 8x^2 + 10x - 3x^2 + 12x - 15
\]

Combine like terms:

1. For \(x^2\): \(-8x^2 - 3x^2 = -11x^2\)
2. For \(x\): \(10x + 12x = 22x\)

So, the simplified polynomial expression is:

\[
2x^3 - 11x^2 + 22x - 15
\]

Thus, the final answer is:

\[
\boxed{2x^3 - 11x^2 + 22x - 15}
\]