Factoring Quadratics (LC = 1, GCF, Diff. of Squares)

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 ax^2 + 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 terms in a polynomial.

Front

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

Back

To factor a trinomial of this form, 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 difference of squares?

Back

The difference of squares is a special factoring case where an expression is in the form a^2 - b^2, which factors to (a + b)(a - b).

Front

Factor the expression: x^2 - 16.

Back

(x + 4)(x - 4) - This is a difference of squares.

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for the GCF of all the terms and factor it out.

Front

Factor the expression: 6x^2 - 27x.

Back

3x(2x - 9) - Factor out the GCF, which is 3x.

Front

What is the factored form of 16p^4 + 4p^3?

Back

4p^3(4p + 1) - Factor out the GCF, which is 4p^3.

Front

How do you factor k^2 - 8k - 20?

Back

(k + 2)(k - 10) - Find two numbers that multiply to -20 and add to -8.