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