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).

Tags

CCSS.HSA.APR.C.4

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).

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSF-IF.C.7C

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.