Factoring Trinomials

Front

What is the process of factoring a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials. This can often be done by finding two numbers that multiply to the constant term and add to the coefficient of the linear term.

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 a difference of squares?

Back

A difference of squares can be factored using the formula a² - b² = (a - b)(a + b).

Front

What is the standard form of a quadratic trinomial?

Back

The standard form of a quadratic trinomial is ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the discriminant in factoring quadratics?

Back

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

Front

How do you factor a perfect square trinomial?

Back

A perfect square trinomial can be factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

Front

What is the first step in factoring the trinomial 4h² - 17h + 4?

Back

The first step is to identify two numbers that multiply to (4 * 4) = 16 and add to -17. These numbers are -16 and -1.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down a polynomial into its simplest factors, including any common factors and irreducible polynomials.

Front

What is the factored form of n² + 10n + 25?

Back

The factored form is (n + 5)², as it is a perfect square trinomial.

Front

How do you identify the leading coefficient in a trinomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.