Alg2CP 3.0 Factoring by Grouping & Parts Check-Up

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

The GCF is the largest factor that divides two or more numbers or expressions without leaving a remainder.

To factor a quadratic equation, find two numbers that multiply to $$ac$$ and add to $$b$$ , then rewrite the equation as a product of two binomials.

The zero product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ .

Factor the equation as $$(x - 2)(x - 3) = 0$$ , then set each factor to zero: $$x - 2 = 0$$ or $$x - 3 = 0$$ , giving solutions $$x = 2$$ and $$x = 3$$ .

The first step is to group terms that have a common factor and factor them out.

Factor out the GCF, which is $$3x^4$$ , resulting in $$3x^4(x^2 - 11x + 24)$$ .

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor it into simpler binomials.

A binomial is a polynomial with exactly two terms, such as $$x + 5$$ or $$3x^2 - 2$$ .

Find two numbers that multiply to 28 and add to -11, which are -4 and -7. Thus, it factors to $$(x - 4)(x - 7)$$ .