Flashcard 5.1-5.4 Review

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor it into simpler binomials or monomials.

Front

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

Back

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

Front

What is the first step in factoring a polynomial by grouping?

Back

The first step is to group the terms in pairs or sets that can be factored out.

Front

What is the result of factoring the polynomial x³ + 7x² - 2x - 14?

Back

The result is (x² - 2)(x + 7).

Front

What is the significance of the coefficients in polynomial expressions when factoring?

Back

Coefficients can affect the common factors that can be factored out from the polynomial.

Front

How do you factor the expression k⁴ + 7k² + 10?

Back

It can be factored as (k² + 2)(k² + 5).

Front

What is the general form of a cubic polynomial?

Back

A cubic polynomial is generally expressed as ax³ + bx² + cx + d, where a, b, c, and d are constants.

Front

What is the factored form of c³ + 9c² + 18c?

Back

The factored form is c(c + 3)(c + 6).

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form by combining like terms and eliminating unnecessary parentheses.

Front

How do you simplify the expression (6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)?

Back

The simplified expression is 5b⁴ - 2b³ + 4.