Factoring Trinomials

Front

What is a trinomial?

Back

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

Front

How do you factor a trinomial of the form x^2 + bx + c?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are those two numbers.

Front

What is the first step in factoring the trinomial x^2 + 9x - 36?

Back

The first step is to identify two numbers that multiply to -36 and add to 9, which are 12 and -3.

Front

Factor the trinomial: x^2 + 9x - 36.

Back

(x + 12)(x - 3)

Front

What is the area of a rectangle in terms of its dimensions?

Back

The area of a rectangle is calculated by multiplying its length by its width.

Front

If the area of a rectangle is given by a trinomial, how can you find its dimensions?

Back

You can find the dimensions by factoring the trinomial to express it as a product of two binomials.

Front

What is the complete factorization of the trinomial 5x^2 + 10x - 15?

Back

5(x + 3)(x - 1)

Front

How do you check if your factorization is correct?

Back

You can check your factorization by expanding the factors back into a trinomial and verifying if it matches the original expression.

Front

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

Back

The leading coefficient affects the shape and direction of the parabola represented by the trinomial when graphed.

Front

What does it mean to factor by grouping?

Back

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