Factor by Grouping

Front

What is the method of factoring by grouping?

Back

Factoring 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 x³ - 4x² - 4x + 16?

Back

Group the terms: (x³ - 4x²) + (-4x + 16). Factor out common factors: x²(x - 4) - 4(x - 4). The factored form is (x - 4)(x² - 4).

Front

What is the factored form of x³ + 7x² - 2x - 14?

Back

The factored form is (x² - 2)(x + 7).

Front

How can you determine if (x - 3) is a factor of 3x³ + 10x² - x - 12?

Back

Use the Factor Theorem: Substitute x = 3 into the polynomial. If the result is 0, then (x - 3) is a factor. In this case, it is not a factor.

Front

What is the factored form of 7r³ - 8r² + 42r - 48?

Back

The factored form is (r² + 6)(7r - 8).

Front

What is the first step in factoring by grouping?

Back

The first step is to group the polynomial into two parts that can be factored separately.

Front

What is a common factor in the expression 20x³ - 25x² + 4x - 5?

Back

The common factor is 5, which can be factored out from the first two terms and the last two terms.

Front

What is the significance of the Factor Theorem in polynomial factoring?

Back

The Factor Theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0.

Front

How do you factor the expression 20x³ - 25x² + 4x - 5 using grouping?

Back

Group the terms: (20x³ - 25x²) + (4x - 5). Factor out common factors: 5x²(4x - 5) + 1(4x - 5). The factored form is (5x² + 1)(4x - 5).

Front

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

Back

Coefficients are the numerical factors in polynomial terms that can affect the grouping and common factors when factoring.