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 standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the relationship between the coefficients and roots of a trinomial?

Back

The sum of the roots is -b/a and the product of the roots is c/a.

Front

How do you identify the coefficients in a trinomial?

Back

In 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

Look for two numbers that multiply to ac (the product of a and c) and add to b.

Front

Factor the trinomial: x² + 5x + 6

Back

(x + 2)(x + 3)

Front

Factor the trinomial: x² - 7x + 10

Back

(x - 2)(x - 5)

Front

What is the difference between a prime polynomial and a factorable polynomial?

Back

A prime polynomial cannot be factored into simpler polynomials, while a factorable polynomial can.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.