Factoring Trinomials

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 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 ax^2 + bx + c = 0, where a, b, and c are constants.

Front

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

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial.

Front

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

Back

The expression factors to (k + 2)(k + 5).

Front

What is the significance of the coefficients in a trinomial?

Back

The coefficients determine the shape and position of the parabola represented by the trinomial when graphed.

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors.

Front

What are the steps to factor a trinomial of the form x^2 + bx + c?

Back

1. Identify two numbers that multiply to c and add to b. 2. Rewrite the trinomial as (x + m)(x + n), where m and n are the identified numbers.

Front

What is the difference between a factor and a multiple?

Back

A factor is a number that divides another number evenly, while a multiple is the result of multiplying a number by an integer.

Front

How do you check if your factorization is correct?

Back

You can check your factorization by multiplying the factors back together to see if you obtain the original polynomial.