8­2 Multiplying and Factoring factor​
(noun) f a k tur Related Words:​
divide, factorable, factored form Definition:​
A factor is a whole number or variable that divides another whole number with a remainder of 0. Essential Understanding​
You can use the distributive property to multiply a monomial by a polynomial. For example, consider the product 2x (3x + 1) . 2x (3x + 1) = 2x (3x) + 2x (1) = 6x2 + 2x you can show why the multiplication makes sense using the area model at the right Simplify each product. A.) 7x (x + 4) B.) 3m2 (10 + m) (
)
C.) 4x 2x3 − 7x2 + x Essential Understanding​
Factoring a polynomial reverses the multiplication process. When factoring a monomial from a polynomial, the first step is to find the greatest common factor (GCF) of the polynomial’s terms. Find the GCF of the terms of each polynomial. D.) 12x + 20
E.) 45b + 27 F.) 4x3 + 12x − 28 Once you find the GCF of a polynomial’s terms, you can factor it out of the polynomial. Factor each polynomial. G.) 9x − 6 H.) 14n3 − 35n2 + 28 I.) 14x3 − 2x2 + 8x J.) ​
Art​
A circular mirror is surrounded by a square metal frame. The radius of the mirror is 5x . The side length of the metal frame is 15x . What is the area of the metal frame? Write your answer in factored form.