Factoring Trinomials a=1

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of 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 of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you determine if a trinomial is factorable?

Back

A trinomial is factorable if it can be expressed as a product of two binomials with rational coefficients.

Front

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

Back

The sum of the roots is equal to -b/a and the product of the roots is equal to c/a in the trinomial ax² + bx + c.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation; if it is positive, there are two distinct real roots, if zero, one real root, and if negative, no real roots.

Front

What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials.

Front

How do you factor the trinomial n² + 16n + 63?

Back

To factor n² + 16n + 63, find two numbers that multiply to 63 and add to 16, which are 7 and 9. Thus, it factors to (n + 7)(n + 9).

Front

What are the steps to factor a trinomial of the form x² + bx + c?

Back

1. Identify two numbers that multiply to c and add to b. 2. Rewrite the trinomial as a product of two binomials using these numbers.

Front

What is the factored form of x² - 9x + 20?

Back

The factored form of x² - 9x + 20 is (x - 5)(x - 4).