Factoring Trinomials a>1

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of 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 of the form ax² + bx + c?

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 when a > 1?

Back

The first step is to multiply 'a' and 'c' to find the product ac.

Front

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

Back

These two numbers help to split the middle term (bx) into two terms that can be factored by grouping.

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms to factor them more easily.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

How can you check if your factorization is correct?

Back

You can check by multiplying the factors back together to see if you obtain the original trinomial.

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant (b² - 4ac) helps determine the nature of the roots of the quadratic equation.