Factoring Trinomials (a=1)

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax^2 + 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 standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0.

Front

What is the significance of the leading coefficient in a trinomial?

Back

The leading coefficient (a) determines the direction of the parabola and affects the shape of the graph.

Front

How do you determine if a trinomial is prime?

Back

A trinomial is prime if it cannot be factored into the product of two binomials with real coefficients.

Front

What is the process for factoring a trinomial when a=1?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b.

Front

What are the steps to factor the trinomial x^2 - 15x + 36?

Back

1. Identify two numbers that multiply to 36 and add to -15. 2. The numbers are -12 and -3. 3. Write the factors as (x - 12)(x - 3).

Front

What is the factored form of m^2 - 13m + 40?

Back

The factored form is (m - 5)(m - 8).

Front

How can you check if your factorization is correct?

Back

You can check by expanding the factors back to the original trinomial.

Front

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

Back

The roots of a trinomial are the values of x that make the factors equal to zero.