We want to study some polynomials and see if each one of them is constant, linear, quadratic, or cubic.
The solutions are:
1) Cubic.
2) Quadratic.
3) Linear.
4) Constant.
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First, let's define what each of these descriptions means:
- Constant: The polynomial does not depend of x, so it is a polynomial of degree 0.
- Linear: The degree of the polynomial is 1.
- Quadratic: The degree of the polynomial is 2.
- Cubic: The degree of the polynomial is 3.
Where the degree of a polynomial is the maximum exponent of that polynomial. Now that we know this, let's analyze each of the given options:
1) x^3 - 2*x + x^3 = 2*x^3 - 2*x
We can see that the maximum exponent here is 3, thus this is a cubic polynomial.
2) 4*x^2 − 6*x − 8*x^2 = (4 - 8)*x^2 - 6*x = -4*x^2 - 6*x
We can see that the maximum exponent is 2, then this is a quadratic polynomial.
3) 6*x − 6 + 6*x = 12*x - 6
We can see that the maximum exponent here is 1, so this is a linear polynomial.
4) 5 + 4*x^2 − 4*x^2 + 5 = = 10 + (4 - 4)*x^2 = 10
We can see that this does not depend of x, this is a constant polynomial.
If you want to learn more, you can read:
https://brainly.com/question/12850541
