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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

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 method for factoring trinomials of the form x^2 + bx + c?

Back

To factor trinomials of the form x^2 + bx + c, find two numbers that multiply to c and add to b.

Front

How do you factor a trinomial when a is not equal to 1?

Back

When a is not equal to 1, use the method of grouping or trial and error to find two binomials that multiply to the trinomial.

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation; if it's positive, there are two distinct real roots.

Front

What is the factored form of the trinomial x^2 - 8x + 15?

Back

The factored form is (x - 5)(x - 3).

Front

What is the factored form of the trinomial k^2 + 7k + 10?

Back

The factored form is (k + 2)(k + 5).

Front

What is the factored form of the trinomial x^2 - 9x + 20?

Back

The factored form is (x - 5)(x - 4).

Front

What is the factored form of the trinomial 3v^2 - 4v - 7?

Back

The factored form is (3v - 7)(v + 1).