Factoring is when you break a large number down into it's simplest divisible parts. Each one of these parts is called a "factor." So, for example, the number 6 can be evenly divided by four different numbers: 1, 2, 3, and 6. Thus, the factors of 6 are 1, 2, 3, and 6.  The factors of 32 are 1, 2, 4, 8, 16, and 32 Both "1" and the number you're factoring are always factors. So, the factors of a small number, like 3, would simply be 1 and 3. Factors are only the perfectly divisible numbers, or "whole" numbers. You could divide 32 by 3.564, or 21.4952, but this won't lead to a factor, just another decimal. A binomial is simply the addition or subtraction of two numbers, at least one of which contains a variable. Sometimes these variables have exponents, like x2{\displaystyle x^{2}} or 5y4{\displaystyle 5y^{4}}. When first factoring binomials, it can help to reorder equations with ascending variable terms, meaning the biggest exponent is last. For example:   3t+6{\displaystyle 3t+6}  →  6+3t{\displaystyle 6+3t}   3x4+9x2{\displaystyle 3x^{4}+9x^{2}}  →  9x2+3x4{\displaystyle 9x^{2}+3x^{4}}   x2−2{\displaystyle x^{2}-2}  →  −2+x2{\displaystyle -2+x^{2}} Note how the negative sign stays in front of the 2. If a term is subtracted, just keep the negative in front of it. This means you find the highest possible number that both parts of the binomial are divisible by. If you're struggling, simply factor both numbers on their own, then see what the highest matching number is. For example:  Practice Problem:3t+6{\displaystyle 3t+6}.  Factors of 3: 1, 3 Factors of 6: 1, 2, 3, 6. The greatest common factor is 3. Once you know your common factor, you need to remove it from each term. Note, however, that you're simply breaking the terms down, turning each term into a small division problem. If you did it right, both equations will share your factor:   Practice Problem:3t+6{\displaystyle 3t+6}.  Find greatest common factor: 3  Remove factor from both terms:3t3+63=t+2{\displaystyle {\frac {3t}{3}}+{\frac {6}{3}}=t+2} In the last problem, you removed a 3 to get t+2{\displaystyle t+2}. But you weren't just getting rid of the three entirely, simply factoring it out to simplify things. You can't just erase numbers without putting them back! Multiply your factor by the expression to finally finish. For example:   Practice Problem:3t+6{\displaystyle 3t+6}   Find greatest common factor: 3  Remove factor from both terms:3t3+63=t+2{\displaystyle {\frac {3t}{3}}+{\frac {6}{3}}=t+2}   Multiple factor by new expression: 3(t+2){\displaystyle 3(t+2)}  Final Factored Answer: 3(t+2){\displaystyle 3(t+2)} If you did everything correctly, checking that you got it right should be easy. Simply multiply your factor by both individual parts in the parenthesis. If it matches the original, unfactored binomial then you did it all correctly. From start to finish, solve the expression 12t+18{\displaystyle 12t+18} to practice:   Reorganize terms:18+12t{\displaystyle 18+12t}   Find greatest common denominator: 6{\displaystyle 6}   Remove factor from both terms:18t6+12t6=3+2t{\displaystyle {\frac {18t}{6}}+{\frac {12t}{6}}=3+2t}   Multiple factor by new expression: 6(3+2t){\displaystyle 6(3+2t)}   Check Answer: (6∗3)+(6∗2t)=18+12t{\displaystyle (6*3)+(6*2t)=18+12t}
تذكر أساسيات التحليل إلى عوامل. رتب حدود ذات الحدين بطريقة تُسهِّل من قراءتها. أوجد العامل المشترك الأكبر للحدين. اقسم كل حد على العامل المشترك الأكبر. اضرب العامل الذي أوجدته في الناتج لإنهاء التبسيط. تحقق من صحة حلك من خلال ضربه لإيجاد المعادلة الأصلية مرة أخرى.