Factoring Trinomials (a not 1)

Front

What is a trinomial?

Back

A trinomial is a polynomial with 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 general form of factoring a trinomial when a ≠ 1?

Back

The general form is ax² + bx + c = (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you identify the coefficients in a trinomial?

Back

In ax² + bx + c, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the first step in factoring a trinomial?

Back

The first step is to multiply 'a' and 'c' (the leading coefficient and the constant term).

Front

What is the purpose of finding two numbers that multiply to ac and add to b?

Back

These two numbers help in splitting the middle term to facilitate factoring.

Front

How do you factor the trinomial 3v² - 4v - 7?

Back

The factors are (3v - 7)(v + 1).

Front

What is the factored form of 15t² - 27t - 6?

Back

The factored form is 3(5t + 1)(t - 2).

Front

How do you factor 5x² - 13x + 6?

Back

The factors are (5x - 3)(x - 2).

Front

What is the factored form of 2m² + 3m - 9?

Back

The factored form is (m + 3)(2m - 3).