Factoring Trinomials with lead CoefficientRev

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) in a polynomial.

Front

How do you factor a trinomial with a lead coefficient of 1?

Back

For a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b.

Front

How do you factor a trinomial with a lead coefficient greater than 1?

Back

For a trinomial of the form ax² + bx + c, use the method of grouping or trial and error to find two binomials.

Front

What is the first step in factoring the trinomial 4n² - 17n - 15?

Back

Identify the lead coefficient (4), the middle term (-17), and the constant term (-15).

Front

What are the factors of the trinomial 3v² - 4v - 7?

Back

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

Front

What is the significance of the constant term in factoring?

Back

The constant term helps determine the pairs of numbers that multiply to it when factoring.

Front

What is the method of grouping in factoring?

Back

The method of grouping involves rearranging and grouping terms to factor by common factors.

Front

How do you check if your factors are correct?

Back

Multiply the factors back together to see if you obtain the original trinomial.