Algebra (FACTORING OUT THE GCF)

factor

an integer that divides evenly into another; a polynomial that divides evenly into another; the process of writing a polynomial as a product of prime factors.

polynomial

a term or a sum of terms whose variables have whole number exponents.

Factor -3x - 3y - 3z.

-3(x + y + z)

What is the missing expression?
x^8 + 3x^5 = x5(_____)

x^3+3

Factor x^4 y^2 + x^3 y^3.

x^3y^2(x+y)

Factor 16p^4 - 24p^3.

8p^3(2p-3)

Factor -24a^3b^3c^3 - 84a^4b^2c.

-12a^3b^2c(2bc^2 + 7a)

Factor 4n^4 + n^3.

n^3(4n + 1)

Factor 14a - 7b.

7(2a-b)

Factor 30y^2 z + 12yz^2 - 18yz.

6yz(5y + 2z - 3)

Factor -4d^3 + 28d^2 - 4d

-4d(d^2 - 7d + 1)

Factor 5k^2 - 35k^3.

5k^2(1 - 7k)

Factor 3y^2 - 4y.

y(3y - 4)

Factor 2a^5 b + 2a^4 b^2 + 2a^3 b^3

2a^3b(a^2 + ab + b2)

Factor a^2 bc + ab^2 c + abc^2

abc(a + b + c)

Factor 48m - 80n.

16(3m - 5n)

Factor 10x^3 + 8x^2 - 6x.

2x(5x^2 + 4x - 3)

Review

A factor of a polynomial divides evenly into it.
To factor out the GCF of a polynomial, divide out the common factor from each term.
To check factorization of a polynomial, multiply the factors to get the original polynomial.