Factoring Trinomials Special Cases

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be written in the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

How do you identify a perfect square trinomial?

Back

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

Front

Factor the trinomial x² + 16x + 64.

Back

(x + 8)².

Front

What is the factored form of 2n² + 13n + 15?

Back

(2n + 3)(n + 5).

Front

What is the first step in factoring a trinomial?

Back

Identify the coefficients of the quadratic, linear, and constant terms.

Front

What is the difference of squares?

Back

The difference of squares is a special case of factoring that applies to expressions of the form a² - b², which can be factored as (a + b)(a - b).

Front

Factor the expression 25x² - 81.

Back

(5x + 9)(5x - 9).

Front

What is the general form of a trinomial?

Back

A trinomial is generally expressed as ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b² - 4ac) helps determine the nature of the roots of a quadratic equation, which can indicate if it can be factored over the reals.

Front

What are the steps to factor a trinomial of the form ax² + bx + c?

Back

1. Multiply a and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.