Factoring and Solving Trinomials

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 polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 or x - q = 0.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

What is the relationship between the coefficients and roots of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

Solve by factoring: x² + 2x - 24 = 0

Back

x = -6, x = 4

Front

Solve by factoring: a² + 10a + 21 = 0

Back

x = -3, x = -7

Front

Solve by factoring: x² - 9x + 20 = 0

Back

x = 4, x = 5

Front

Factor: k² - 2k - 24

Back

(k + 4)(k - 6)