Question

multiply to simplify the polynomial expression then fill in the blanks (_)
(2x - 3) (x^2- 4x + 5)

_x^3 + _x^2 + _x +_

Answer 1

To simplify the polynomial expression \((2x - 3)(x^2 - 4x + 5)\), we can distribute each term in the first factor across all terms in the second factor.

Let's do that step-by-step:

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

Putting it together, from the \(2x\):
\[
2x^3 - 8x^2 + 10x
\]

2. Next, distribute \(-3\) across \(x^2 - 4x + 5\):
- \(-3 \cdot x^2 = -3x^2\)
- \(-3 \cdot (-4x) = 12x\)
- \(-3 \cdot 5 = -15\)

Putting it together, from \(-3\):
\[
-3x^2 + 12x - 15
\]

3. Now we combine all of these results:
\[
2x^3 + (-8x^2 - 3x^2) + (10x + 12x) - 15
\]
This simplifies to:
\[
2x^3 - 11x^2 + 22x - 15
\]

Now we can fill in the blanks:
\[
2x^3 + (-11)x^2 + (22)x + (-15)
\]

Thus, the filled-in blanks are:
- First blank: **2**
- Second blank: **-11**
- Third blank: **22**
- Fourth blank: **-15**

Final answer:
\[
(2, -11, 22, -15)
\]