Question

Multiply to simplify the polynomial expression (2x−3)(x2−4x+5)
.(1 point)
x3 +

x2 +

x +

Answer 1

To simplify the polynomial expression \((2x−3)(x^2−4x+5)\), we will use the distributive property (often called the FOIL method for binomials). We will distribute \(2x\) and \(-3\) to each term inside the second polynomial.

1. Distributing \(2x\):
- \(2x \cdot x^2 = 2x^3\)
- \(2x \cdot (-4x) = -8x^2\)
- \(2x \cdot 5 = 10x\)

2. Distributing \(-3\):
- \(-3 \cdot x^2 = -3x^2\)
- \(-3 \cdot (-4x) = 12x\)
- \(-3 \cdot 5 = -15\)

Now we combine all these results together:
\[
2x^3 - 8x^2 + 10x - 3x^2 + 12x - 15
\]

Now combine like terms:
- The \(x^3\) term is \(2x^3\).
- The \(x^2\) terms: \(-8x^2 - 3x^2 = -11x^2\).
- The \(x\) terms: \(10x + 12x = 22x\).
- The constant term is \(-15\).

So, the simplified polynomial expression is:
\[
2x^3 - 11x^2 + 22x - 15
\]

Based on the format asked in the question, the answer breaks down as follows:
- \(x^3\) term: \(2\)
- \(x^2\) term: \(-11\)
- \(x\) term: \(22\)
- Constant term: \(-15\)

Thus, the ultimately simplified polynomial is:
\[
2x^3 - 11x^2 + 22x - 15
\]