Solving Polynomial Equations by Factoring 5th P

Front

What is the difference of cubes formula?

Back

The difference of cubes formula states that a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

How do you factor the expression x^3 - 343?

Back

Using the difference of cubes formula, x^3 - 343 can be factored as (x - 7)(x^2 + 7x + 49).

Front

What is the grouping method in factoring?

Back

The grouping method involves rearranging and grouping terms in a polynomial to factor it into simpler binomials.

Front

How do you factor the expression 4p³ + 8p² + 3p + 6 by grouping?

Back

By grouping, you can factor it as (4p² + 3)(p + 2).

Front

What is the first step in solving polynomial equations by factoring?

Back

The first step is to set the equation equal to zero.

Front

How do you solve the equation x^3 - 3x^2 - 5x + 15 = 0 by factoring?

Back

You can factor it to find the roots, which are x = 3, x = ±√5.

Front

What are the roots of the polynomial equation x^4 + 4x^3 + 3x^2 = 0?

Back

The roots are x = 0, x = -3, and x = -1.

Front

What is the significance of finding roots in polynomial equations?

Back

Finding roots helps determine the values of x where the polynomial equals zero, which is essential for solving equations.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

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