Factoring a=1

Front

What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials. This is typically done by finding two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, usually in the form ax^2 + bx + c.

Front

Can every trinomial be factored into two binomials?

Back

No, not every trinomial can be factored into two binomials. Some trinomials are prime and cannot be factored over the integers.

Front

What is the GCF (Greatest Common Factor) and how is it used in factoring?

Back

The GCF is the largest factor that divides all terms in a polynomial. It is used in factoring by first factoring out the GCF before factoring the remaining polynomial.

Front

How do you factor the expression r^2 - 16r + 60?

Back

To factor r^2 - 16r + 60, find two numbers that multiply to 60 and add to -16. The factors are -6 and -10, so the expression factors to (r - 6)(r - 10).

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, such as (x + y) or (a - b).

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down a polynomial into its simplest form, where no further factoring is possible.

Front

What is the significance of the coefficient 'a' in a quadratic equation ax^2 + bx + c?

Back

The coefficient 'a' determines the direction and width of the parabola represented by the quadratic equation. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How do you factor the expression k^2 + 7k + 10?

Back

To factor k^2 + 7k + 10, find two numbers that multiply to 10 and add to 7. The factors are 2 and 5, so the expression factors to (k + 2)(k + 5).

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 = a^2 + 2ab + b^2.