Factoring Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax² + bx + c.

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials.

Front

What is the general form of a factored trinomial?

Back

The general form is (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you identify the coefficients in a trinomial?

Back

In the trinomial ax² + bx + c, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the first step in factoring a trinomial?

Back

The first step is to identify the coefficients a, b, and c from the trinomial.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b² - 4ac) helps determine the nature of the roots of the trinomial; if it's positive, there are two distinct real roots.

Front

How can you factor a trinomial when a = 1?

Back

If a = 1, you look for two numbers that multiply to c and add to b.

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms to factor by pairs.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, e.g., (x + a)² = x² + 2ax + a².

Front

How do you factor the trinomial 3a² + 4a + 1?

Back

The factored form is (3a + 1)(a + 1).