factor 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

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 the two numbers.

Front

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

Back

(x + 12)(x - 3)

Front

What is the first step in factoring a trinomial?

Back

The first step is to identify the coefficients a, b, and c in the trinomial ax^2 + bx + c.

Front

Factor the trinomial: n^2 + 5n - 6

Back

(n - 1)(n + 6)

Front

What does it mean to factor a polynomial?

Back

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

Front

Factor the trinomial: a^2 - a - 12

Back

(a - 4)(a + 3)

Front

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

Back

The roots of a trinomial are the values of x that make the trinomial equal to zero, and they correspond to the values that make each factor equal to zero.

Front

Factor the trinomial: x^2 - 8x + 15

Back

(x - 5)(x - 3)

Front

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

Back

The leading coefficient (a) affects the direction of the parabola represented by the trinomial when graphed.