Higher-Degree Polynomials. Lesson 7.7. Polynomials with degree 3 or higher are called higher-degree polynomials.
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A polynomial function with three x-intercepts has too many x-intercepts to be a quadratic function. It could be a 3rd-, 4th-, 5th-, or higher-degree polynomial function. Consider a 3rd-degree polynomial function, because
that is the lowest degree that has three x-intercepts. Use the x-intercepts to write the equation y=a(x-3)(x-5)(x+4), where a≠0.
For a polynomial function with real coefficients, complex zeros occur in conjugate pairs, so x=3-4i must also be a zero. In factored form the polynomial function of the lowest degree is y=(x-2)(x+5)[x-(3+4i)][x-(3-4i)]
Multiplying the last two factors to eliminate complex numbers gives y=(x-2)(x+5)(x2-6x+25).
Multiplying all factors gives the polynomial function in general form: y=x4-3x3-3x2 +135x-250
Any polynomial function of degree n always has n complex zeros (including repeated zeros) and at most n x-intercepts. Remember that complex zeros of polynomial functions with real coefficients always come in conjugate pairs.