Factoring Trinomials (a=1)

Front

What is a trinomial?

Back

A trinomial is a polynomial with 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 is ax^2 + bx + c, where a, b, and c are constants.

Front

What is the first step in factoring a trinomial when a=1?

Back

Identify two numbers that multiply to c and add to b.

Front

Factor the trinomial: x^2 - 10x + 24

Back

(x - 6)(x - 4)

Front

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

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and they correspond to the factors of the polynomial.

Front

How do you check if your factorization is correct?

Back

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

Front

Factor the trinomial: r^2 - 8r + 15

Back

(r - 5)(r - 3)

Front

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

Back

The leading coefficient determines the direction of the parabola when graphed.

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into simpler components, while expanding is multiplying out the components.