Find the GCF of the terms of each polynomial. 12 x+20 |...

Name: Problem 15, Chapter 8: Algebra 1 Common Core
Uploaded: 2020-03-29T02:55:42-08:00
Duration: 2 min 52 s
Channel: Jason Taylor-Pestell
Description: Find the GCF of the terms of each polynomial. 12 x+20

Key Concepts

Greatest Common Factor (GCF)

The GCF is the largest expression (whether a number, a variable, or a combination of both) that divides each term of a given expression without leaving a remainder. Understanding the GCF is fundamental in simplifying expressions and solving equations, as it allows you to factor out shared components from different terms in a polynomial.

Polynomial Terms

Polynomials are algebraic expressions made up of terms, which are individual parts usually separated by addition or subtraction. Each term consists of a numerical coefficient multiplied by variables raised to non-negative integer exponents. Recognizing and analyzing these terms is key to performing operations such as factoring and simplifying the expression.

Common Factors

When dealing with multiple terms in an expression, common factors are those parts that appear in every term. These factors can be numerical, variable, or a combination of both. Identifying these factors is a critical step in the process of factoring, as it allows for the extraction of the greatest common factor, which simplifies the overall expression.

Factoring Polynomials

Factoring is the process of rewriting a polynomial as a product of simpler expressions. By extracting the GCF from a set of terms, you reduce the polynomial into a form that is easier to manipulate algebraically, which can be particularly useful for solving equations and simplifying complex expressions.

Transcript

00:01 All right, in this problem, we are asked to find the greatest common factor, or gcf, of 12x plus 20.

00:07 And so i'm going to use the strategy double division or upside down division to find the common factors of 12x and 20.

00:20 To begin with, i'm going to look at the variables.

00:23 I notice that they don't both have variables, which means i cannot put a variable in the common factors, since it's not in common.

00:29 So then i can just focus on the numbers, 12 and 20.

00:33 Some numbers that come to mind are i know that 12 can be made with 2 and so can 20.

00:38 I also know that 12 could be made using 4 and so can 20.

00:44 So i could use 2 or 4.

00:46 Now, in previous examples that i've shown, i've always done the highest number that i can think of.

00:50 But i'm going to show what would happen if you did not think of that and show how powerful this particular strategy is for finding the greatest common factor.

00:58 So let's say that two was the biggest i could think of right now.

01:02 I would divide each of the terms by two and see what happens.

01:06 So two goes into 12, six times.

01:08 The answer goes below.

01:10 The x drops down because i didn't divide any x's out, plus two goes into 20, 10 times.

01:18 And so i'll place my 10 here.

01:20 Now i'm at the next level of double division.

01:23 So at this level, i'm going to see what makes these numbers.

01:27 I know that i can count by twos to get to six, and also to 10.

01:30 And so i'm going to put a two on the outside again...