Factoring Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial with 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 if a trinomial can be factored over the integers.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the trinomial has two distinct real roots and can be factored.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the trinomial has one real root (a perfect square) and can be factored as a square of a binomial.

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the trinomial cannot be factored over the integers.

Front

Factor the trinomial: 2m² + 3m - 9

Back

(m + 3)(2m - 3)