Factoring Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax^2 + 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 (x + p)(x + q), where p and q are numbers that satisfy the equation.

Front

How do you identify the coefficients in a trinomial?

Back

In the trinomial ax^2 + bx + c, 'a' is the coefficient of x^2, '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 relationship between the roots and the factors of a trinomial?

Back

The roots of a trinomial are the values of x that make the trinomial equal to zero, and they correspond to the values of p and q in the factored form (x + p)(x + q).

Front

How can you check if your factorization is correct?

Back

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

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b^2 - 4ac) helps determine the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the factoring method for a trinomial when a = 1?

Back

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

Front

What is the factoring method for a trinomial when a ≠ 1?

Back

When a ≠ 1, use the 'ac method' where you multiply a and c, find two numbers that multiply to ac and add to b, then rewrite the trinomial.