Factoring Quadratic Equations

Front

What is a perfect square trinomial?

Back

Front

How do you identify a perfect square trinomial?

Back

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

Front

Factor the expression: x^2 + 16x + 64

Back

(x + 8)^2

Front

What is the factored form of a quadratic equation?

Back

Front

How do you factor the quadratic expression x^2 - 17x + 72?

Back

To factor, find two numbers that multiply to 72 and add to -17. The factors are -9 and -8, so the expression factors to (x - 9)(x - 8).

Front

What is the significance of the roots in a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They represent the x-intercepts of the graph of the quadratic function.

Front

What does it mean to factor completely?

Back

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

Front

Factor the expression: x^2 - 25

Back

(x - 5)(x + 5) (This is a difference of squares.)

Front

What is the difference between a binomial and a trinomial?

Back

A binomial is a polynomial with two terms, while a trinomial has three terms.

Front

How do you factor the expression: r^2 + 6r + 9?

Back

(r + 3)^2 (This is a perfect square trinomial.)