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

How do you determine if a trinomial is prime?

Back

A trinomial is prime if it cannot be factored into the product of two binomials with real coefficients.

Front

What is the relationship between the coefficients and 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 ax^2 + bx + c.

Front

What is the first step in factoring a trinomial of the form x^2 + bx + c?

Back

Identify two numbers that multiply to c and add to b.

Front

How do you factor the trinomial x^2 - 15x + 36?

Back

Find two numbers that multiply to 36 and add to -15, which are -12 and -3. Thus, it factors to (x - 12)(x - 3).

Front

What is the factored form of m^2 - 13m + 40?

Back

The factored form is (m - 5)(m - 8).

Front

What is the factored form of p^2 + 18p + 45?

Back

The factored form is (p + 15)(p + 3).

Front

What is the factored form of n^2 - 12n + 35?

Back

The factored form is (n - 7)(n - 5).