A polynomial with a degree of 4 is an expression that includes a variable raised to the fourth power, along with non-negative integer powers of that variable, and possibly constant terms. The general form of such a polynomial can be expressed as:
P(x) = ax4 + bx3 + cx2 + dx + e
In this expression:
- a, b, c, d, e are constants, where a cannot be zero since that would reduce the degree of the polynomial.
- x represents the variable.
Here’s an example of such a polynomial:
P(x) = 2x4 – 3x3 + 5x2 + 7
This polynomial has a degree of 4, which is determined by the highest power of the variable x, which is 4 in this case.
Polynomials of degree 4 can have various shapes and roots depending on the values of their coefficients (a, b, c, d, and e). They are commonly used in algebra and can be graphed to show their behavior across the coordinate plane.