7.5 Factoring Trinomials A=1

Front

What is a trinomial?

Back

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

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the first step in factoring a trinomial of the form x^2 + bx + c?

Back

Identify two numbers that multiply to c and add to b.

Front

Factor the trinomial: x^2 + 5x + 6

Back

(x + 2)(x + 3)

Front

What is the difference of squares?

Back

The difference of squares is a special case of factoring, expressed as a^2 - b^2 = (a - b)(a + b).

Front

Factor the trinomial: x^2 - 9

Back

(x - 3)(x + 3)

Front

What is the role of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the method of factoring, especially if a ≠ 1.

Front

Factor the trinomial: 2x^2 + 8x + 6

Back

2(x + 1)(x + 3)

Front

What is the significance of the zero product property?

Back

If the product of two factors equals zero, at least one of the factors must be zero.