Solving Higher Degree Polynomials & Intercepts

Front

What is the maximum number of zeros a polynomial function can have?

Back

The maximum number of zeros a polynomial function can have is equal to its degree.

Front

What is the degree of the polynomial P(x) = 3x^4 + 4x - 8?

Back

The degree of the polynomial P(x) = 3x^4 + 4x - 8 is 4.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for the variable.

Front

Solve for the values of x: (2x - 1)(x + 4) = 0

Back

x = 1/2, -4.

Tags

CCSS.HSA-REI.B.4B

Front

What are complex zeros in polynomial functions?

Back

Complex zeros are solutions to polynomial equations that include imaginary numbers.

Front

Find all zeros of the polynomial function P(x) = x^3 + 6x^2 + 9x + 54.

Back

The zeros are -6, 3i, -3i.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Tags

CCSS.HSN.CN.C.9

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n ≠ 0.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

What is the relationship between the degree of a polynomial and the number of its intercepts?

Back

A polynomial of degree n can have at most n real intercepts.

Tags

CCSS.HSF-IF.C.7C