Factoring Trinomials a=1

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 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 is the relationship between the coefficients and roots of a quadratic equation?

Back

For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

How do you factor the trinomial x^2 + bx + c?

Back

To factor x^2 + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are those numbers.

Front

What is the factored form of d^2 - 10d + 25?

Back

The factored form is (d - 5)(d - 5) or (d - 5)^2.

Front

How do you identify the coefficients in a trinomial?

Back

In a 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 significance of the discriminant in factoring quadratics?

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

What is the factored form of x^2 + 5x + 4?

Back

The factored form is (x + 4)(x + 1).

Front

What is the factored form of a^2 - a - 12?

Back

The factored form is (a - 4)(a + 3).