Factor Trinomials

Front

What is a trinomial?

Back

A trinomial is a polynomial with 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 standard form of a quadratic trinomial?

Back

The standard form is ax^2 + bx + c, where a, b, and c are constants.

Front

How do you identify the coefficients in a trinomial?

Back

In 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 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 factors in the form (x - r1)(x - r2).

Front

What is the first step in factoring a trinomial?

Back

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

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b^2 - 4ac) determines 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

How do you factor the trinomial x^2 - 8x + 15?

Back

The factors are (x - 5)(x - 3).

Front

What is the factored form of 4n^2 - 17n - 15?

Back

The factored form is (n - 5)(4n + 3).

Front

How do you factor 7r^3 - 8r^2 + 42r - 48?

Back

The factored form is (r^2 + 6)(7r - 8).