Mixed Factoring

Front

What is the process of factoring a trinomial of the form x^2 + bx + c?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b. Rewrite the trinomial as (x + m)(x + n), where m and n are the two numbers.

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a^2 - b^2 = (a + b)(a - b).

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for a greatest common factor (GCF) among the terms.

Front

What is the factored form of x^2 - 9?

Back

The factored form of x^2 - 9 is (x + 3)(x - 3).

Front

How do you factor the expression x^3 - 5x^2 + 5x - 25?

Back

To factor x^3 - 5x^2 + 5x - 25, group the terms: (x^3 - 5x^2) + (5x - 25) = x^2(x - 5) + 5(x - 5) = (x^2 + 5)(x - 5).

Front

What is the factored form of n^2 + 16n + 63?

Back

The factored form of n^2 + 16n + 63 is (n + 7)(n + 9).

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What is the significance of the coefficients in a trinomial when factoring?

Back

The coefficients in a trinomial help determine the numbers that will multiply to the constant term and add to the linear coefficient.

Front

What is the method for factoring by grouping?

Back

Factoring by grouping involves rearranging the terms of a polynomial, grouping them into pairs, and factoring out the common factors from each group.

Front

What is the factored form of 20x^3 - 25x^2 + 4x - 5?

Back

The factored form of 20x^3 - 25x^2 + 4x - 5 is (5x^2 + 1)(4x - 5).

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.