The classification of the polynomials are:
(1) Cubic
(2) Quadratic
(3) Linear
(4) Constant
How to classify the polynomials?
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) x³ - 2x + x³ = 2x³ - 2x
We can see that the maximum exponent here is 3, thus this is a cubic polynomial.
2) 4x² − 6x − 8x² = -4x² - 6x
We can see that the maximum exponent is 2, then this is a quadratic polynomial.
3) 6x − 6 + 6x = 12x - 6
We can see that the maximum exponent here is 1, so this is a linear polynomial.
4) 5 + 4x² − 4x² + 5 =
10 + (4 - 4)x² = 10
We can see that this does not depend of x, this is a constant polynomial.
Complete question is:
Classify each polynomial as constant, linear, quadratic, or cubic. Combine like terms first.
1. x³ − 2x + x³
A. Constant
B. Linear
C. Quadratic
D. Cubic
2. 4x² − 6x − 8x²
A. Constant
B. Linear
C. Quadratic
D. Cubic
3. 6x − 6 + 6x
A. Constant
B. Linear
C. Quadratic
D. Cubic
4. 5 + 4x² − 4x² + 5
A. Constant
B. Linear
C. Quadratic
D. Cubic