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 factoring a trinomial?

Back

The general form is (x + p)(x + q) where p and q are numbers that add to b and multiply to c.

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.

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.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the trinomial has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the trinomial has exactly one real root (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the trinomial has no real roots (the roots are complex).

Front

How can you check if your factorization is correct?

Back

You can check by multiplying the binomials back together to see if you get the original trinomial.