Factoring Trinomials

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides all the terms in an expression.

Front

How do you factor a trinomial of the form ax² + bx + c?

Back

To factor a trinomial, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the middle term using these numbers and factor by grouping.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring case where an expression is in the form a² - b², which can be factored as (a + b)(a - b).

Front

What is the factored form of 3x² + 18x + 15?

Back

3(x + 5)(x + 1) is the factored form.

Front

How do you factor 3x² - 75?

Back

Factor out the GCF first: 3(x² - 25), then recognize it as a difference of squares: 3(x + 5)(x - 5).

Front

What is the factored form of x² - 16x + 48?

Back

(x - 12)(x - 4) is the factored form.

Front

What is the factored form of 3x² + 23x - 8?

Back

(3x - 1)(x + 8) is the factored form.

Front

What is the factored form of 6x² - 16x + 8?

Back

2(3x - 2)(x - 2) is the factored form.