Factor by Grouping

Front

What is the method of factor by grouping?

Back

Factor by grouping is a technique used to factor polynomials by grouping terms with common factors and then factoring out the common binomial.

Front

How do you factor the expression 7r³ - 8r² + 42r - 48?

Back

The expression can be factored as (r² + 6)(7r - 8) by grouping the first two terms and the last two terms.

Front

What is the first step in factoring by grouping?

Back

The first step is to group the terms in pairs that have common factors.

Front

What is the factored form of 30x³ + 15x² - 18x - 9?

Back

The factored form is 3(5x² - 3)(2x + 1).

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means expressing it as a product of its irreducible factors.

Front

How do you identify common factors in a polynomial?

Back

Common factors can be identified by looking for the greatest common divisor of the coefficients and the lowest power of the variable present in each term.

Front

What is the factored form of 20x³ - 25x² + 4x - 5?

Back

The factored form is (5x² + 1)(4x - 5).

Front

What is the significance of the Rational Root Theorem in factoring polynomials?

Back

The Rational Root Theorem helps identify possible rational roots of a polynomial, which can be tested to find factors.

Front

How do you solve the equation x³ + 7x² - 2x - 14 = 0?

Back

To solve this equation, you can use factoring or synthetic division to find the roots, which are ±√2 and -7.

Front

What is the factored form of x³ - 5x² + 5x - 25?

Back

The factored form is (x² + 5)(x - 5).