Write polynomial from factors

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What does it mean for a number to be a zero of a polynomial?

Back

A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.

Front

How do you find a polynomial from its zeros?

Back

To find a polynomial from its zeros, you can use the fact that if r is a zero, then (x - r) is a factor of the polynomial. Multiply the factors corresponding to all zeros to get the polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

If a polynomial has a degree of 3, how many zeros can it have?

Back

A polynomial of degree 3 can have up to 3 zeros, counting multiplicities.

Front

What is the conjugate root theorem?

Back

The conjugate root theorem states that if a polynomial has real coefficients and a complex root a + bi, then its conjugate a - bi is also a root.

Front

What is the relationship between the roots and factors of a polynomial?

Back

Each root of a polynomial corresponds to a factor of the form (x - r), where r is the root.

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, which corresponds to the zeros of the function.

Front

What is the significance of imaginary roots in polynomials?

Back

Imaginary roots of polynomials always come in conjugate pairs when the coefficients are real.

Front

How do you express a polynomial with given zeros 2 and -3?

Back

The polynomial can be expressed as P(x) = (x - 2)(x + 3).