Factoring out a GCF

Factoring Out a GCF

What is Factoring?

• Separating a simplified polynomial back into a product.

• It is like "splitting" an expression into a multiplication of simpler expressions.

• Simplified Form 4a²+8a ---> Factored Form 4a(a+2)

• Polynomials that cannot be factored are called PRIME !

There are several factoring methods; the approach depends on the polynomial. We will start by identifying and factoring out the greatest common factor (GCF) of the polynomial.

• Factor 3x+12.

• Both terms can be divided by 3.

• Fully factored it is 3(x+4) You can check this by multiplying it back. You should get what you started with.

Factor 8m+36n

• Both terms can be divided by 4

• 4(2m+9n)

• The terms left in the parentheses should NOT have any more common factors.

Multiple Choice

Factor 7y-7.

• 7(y-7)

• 1(7y-7)

• Prime

Factor 4y²-24y

• All terms can be divided by 4, and all terms contain at least 1 y.

• We factor OUT a 4y and the leftovers stay in the parentheses.

• 4y(y-6)

Factor 21cd+3d

• Both terms can be divided by 3 and they both contain at least 1 factor of d.

• We factor OUT a 3d and the leftovers stay in the parentheses.

• 3d(7c+1)

Multiple Choice

Factor completely 14gh-18h

• 2(7gh-9h)

• 2h(7g-9)

• 14h(g-4)

Multiple Choice

Factor 5x-13y

• x(5-13y)

• 5(x-8y)

• Prime

Factor 2x²y – 2xy²+ 4xy

• All terms can be divided by 2. They all contain at LEAST 1 x and 1 y

• They all contain at LEAST 1 x and 1 y

• So, we factor OUT a 2xy... and the leftovers go in parentheses.

• 2xy(x-y+2)

Factor 9r⁸ – 18r²s – 24rs²

• All terms can be divided by 3.

• All terms have at least 1 factor of r.

• Factor OUT 3r and leave the rest in parentheses.

• 3r(3r⁷-6rs-8s²)

Multiple Choice

Factor 6y⁴ + 14y³ – 10y²

• y²(6y²+14y-10)

• 2y²(3y²+7y-5)

• y(6y⁴+14y³-10y)