Factoring Trinomials with lead Coefficient

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 lead coefficient in a trinomial?

Back

The lead coefficient is the coefficient of the term with the highest degree (the first term when written in standard form).

Front

How do you identify the lead coefficient in 4n² - 17n - 15?

Back

The lead coefficient is 4, which is the coefficient of n².

Front

What is the general form of factoring a trinomial with a lead coefficient of 1?

Back

For a trinomial in the form x² + bx + c, it factors to (x + p)(x + q) where p and q are numbers that add to b and multiply to c.

Front

What is the process for factoring a trinomial with a lead coefficient greater than 1?

Back

1. Multiply the lead coefficient by the constant term. 2. Find two numbers that multiply to this product and add to the middle coefficient. 3. Rewrite the trinomial and factor by grouping.

Front

Factor the trinomial: 4n² - 17n - 15.

Back

(n - 5)(4n + 3) is the factored form.

Front

Factor the trinomial: 5x² + 17x + 6.

Back

(5x + 2)(x + 3) is the factored form.

Front

What is the first step in factoring 2m² + 3m - 9?

Back

Identify the lead coefficient (2), the middle term (3), and the constant (-9).

Front

Factor the trinomial: 3n² - 15n + 18 completely.

Back

3(n - 3)(n - 2) is the completely factored form.