Factor Trinomials

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 means rewriting it as a product of two binomials.

Front

What is the general form of a factored trinomial?

Back

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

Front

How do you identify the coefficients in a trinomial?

Back

In the trinomial 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 look for a common factor in all terms.

Front

How do you factor the trinomial 3n² - 15n + 18?

Back

Factor out the greatest common factor (3) to get 3(n² - 5n + 6), then factor the quadratic to get 3(n - 3)(n - 2).

Front

What is the significance of the quadratic formula in factoring?

Back

The quadratic formula can be used to find the roots of a trinomial, which helps in factoring it.

Front

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

Back

If r1 and r2 are the roots of the trinomial, it can be factored as a(x - r1)(x - r2).

Front

How do you factor the trinomial 5x² - 15x + 10?

Back

Factor out the greatest common factor (5) to get 5(x² - 3x + 2), then factor the quadratic to get 5(x - 2)(x - 1).

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms to factor polynomials.