Unit 4B Skills Check - Polynomial Equations and Expressions

Front

What is the maximum number of solutions a polynomial can have based on its degree?

Back

A polynomial of degree n can have at most n solutions.

Front

Given the polynomial f(x) = 5x^4 + 27x^3 + 17x - 28, what is its degree?

Back

The degree of the polynomial is 4.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors.

Front

How do you determine the number of solutions for the polynomial f(x) = 35x^4 + 2x^6 + 64x^2 - 17?

Back

The number of solutions is determined by the degree of the polynomial, which is 6.

Front

What is the factored form of the polynomial f(x) = (x+4)(x+1)^2(x-2)(x-4)?

Back

This is the factored form of the polynomial, showing its roots.

Front

What is the sum of the roots of the polynomial f(x) = 5x^4 + 27x^3 + 17x - 28?

Back

The sum of the roots can be found using Vieta's formulas, which relate the coefficients of the polynomial to sums and products of its roots.

Front

What is the formula for factoring a sum of cubes?

Back

The formula for factoring a sum of cubes a^3 + b^3 is (a + b)(a^2 - ab + b^2).

Front

What is the formula for factoring a difference of cubes?

Back

The formula for factoring a difference of cubes a^3 - b^3 is (a - b)(a^2 + ab + b^2).

Front

How do you factor the polynomial 27x^3 + 8?

Back

You can factor it as (3x + 2)(9x^2 - 6x + 4) using the sum of cubes formula.

Front

What is the factored form of 8x^3 - 1?

Back

The factored form is (2x - 1)(4x^2 + 2x + 1) using the difference of cubes formula.