HW23 - Polynomial practice

Front

What are the zeros of the polynomial f(x) = (x-5)(2x+3)(7x-4)(x+6)?

Back

The zeros are x = 5, -3/2, 4/7, -6.

Front

What is the missing term when dividing (2x^3 + 5x^2 + 9) by (x + 3)?

Back

The missing term is x.

Front

How can you determine if (x-2) is a factor of f(x) = x^3 - 8x^2 + 14x - 4?

Back

Use the Factor Theorem: if f(2) = 0, then (x-2) is a factor.

Front

What number should be placed in the left-hand box for synthetic division of x^3 + 12x^2 + 20x - 96 by x - 2?

Back

The number is 2.

Front

How many zeros are needed in the top row for synthetic division of x^6 + 4x^3 + 2?

Back

Four zeros are needed.

Front

Define a polynomial.

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of f(x) if and only if f(c) = 0.

Front

How do you find the degree of a polynomial?

Back

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