Question

What are the different types of terms that appear in the polynomial expression?
(Select all the apply)
2(x2−x)+6x−3−7x
Constant
Linear
Quadratic
Cubic

Answer 1

To determine the types of terms that appear in the polynomial expression \( 2(x^2 - x) + 6x - 3 - 7x \), let's simplify it first.

1. Expand \(2(x^2 - x)\):
\[
2(x^2 - x) = 2x^2 - 2x
\]

2. Combine all the terms:
\[
2x^2 - 2x + 6x - 3 - 7x
\]
\[
= 2x^2 + (-2x + 6x - 7x) - 3
\]
\[
= 2x^2 - 3
\]

Now, the simplified polynomial is \(2x^2 - 3\).

Next, we identify the types of terms present in this polynomial:

- **Constant term**: \(-3\) (the term without \(x\))
- **Linear term**: There is no linear term (term with \(x^1\))
- **Quadratic term**: \(2x^2\) (the term with \(x^2\))
- **Cubic term**: There is no cubic term (term with \(x^3\))

Based on the above, the types of terms present in the polynomial are:

- **Constant**: Yes
- **Linear**: No
- **Quadratic**: Yes
- **Cubic**: No

So the correct selections are:

- Constant
- Quadratic