Learn about a factorization method called "grouping." For example, we can use grouping to write 2x²+8x+3x+12 as (2x+3)(x+4).
Log in Nin 8 years agoPosted 8 years ago. Direct link to Nin's post “This may sound a bit dumb...” This may sound a bit dumb, but is there any significant difference between factoring, grouping trinomials, difference of squares, and GCF? • (43 votes) Copperhead514 5 years agoPosted 5 years ago. Direct link to Copperhead514's post “Nothing significant, but ...” Nothing significant, but there are important (however small) differences and they are used for different things. (35 votes) daleighellison 7 years agoPosted 7 years ago. Direct link to daleighellison's post “How would you work out th...” How would you work out the problem if there were only 3 terms? • (18 votes) Ian Pulizzotto 7 years agoPosted 7 years ago. Direct link to Ian Pulizzotto's post “Find two numbers that add...” Find two numbers that add to the middle coefficient and multiply to give the product of the first and last coefficients (or constants). This is called the ac method. Example: Factor 6x^2 + 19x + 10. 6x^2 + 19x + 10 = 6x^2 + 15x + 4x + 10 Have a blessed, wonderful day! rama 6 years agoPosted 6 years ago. Direct link to rama's post “what the meaning of GCF?” what the meaning of GCF? • (2 votes) Kim Seidel 6 years agoPosted 6 years ago. Direct link to Kim Seidel's post “GCF is the abbreviation f...” GCF is the abbreviation for Greatest Common Factor. (25 votes) Seraj shaheen a year agoPosted a year ago. Direct link to Seraj shaheen's post “Wow I got this better tha...” Wow I got this better than how I learned it in school thanks Sal! • (11 votes) louisaandgreta 3 years agoPosted 3 years ago. Direct link to louisaandgreta's post “Why are they called quadr...” Why are they called quadratics? They are typically trinomials with a leading term raised to the second degree. • (2 votes) lemonomadic 3 years agoPosted 3 years ago. Direct link to lemonomadic's post “Quadratics actually are d...” Quadratics actually are derived from the Latin word, 'quadratum', which literally means 'square'. Dannon Foster 2 years agoPosted 2 years ago. Direct link to Dannon Foster's post “Lets say there is no GCF ...” Lets say there is no GCF in anything. Then What? • (4 votes) AuroraAlberts a year agoPosted a year ago. Direct link to AuroraAlberts's post “There is always a GCF, it...” There is always a GCF, it just depends on how many there are. Let's take 4 and 3. The only common factor here is 1, so 1 is the GCF of 4 and 3! So to answer your question, if you can't find the greatest common factor of two numbers, it's 1. (9 votes) Hafsa Mohamed 7 years agoPosted 7 years ago. Direct link to Hafsa Mohamed's post “In problem 3, I solved th...” In problem 3, I solved the expression and got the answer (4x+2)(2x+1.5). It said my answer was correct, but when I checked my answer, I got the same expression. What did I do wrong? • (6 votes) smitters a year agoPosted a year ago. Direct link to smitters's post “u used _1.5_ which is not...” u used 1.5 which is not a natural number. Therefore answer is incorrect. Correct answer must include only natural numbers: (3x+2)(3x+4) (2 votes) Joshua Zanetta a year agoPosted a year ago. Direct link to Joshua Zanetta's post “I'm getting this!” I'm getting this! • (6 votes) YourLordJoyBoy89 4 months agoPosted 4 months ago. Direct link to YourLordJoyBoy89's post “I want to get it too, how...” I want to get it too, how can I though? (3 votes) tarasandbeck 10 months agoPosted 10 months ago. Direct link to tarasandbeck's post “Hi Professor,Why dont yo...” Hi Professor, • (6 votes) Gonzalo Sandmeier 10 months agoPosted 10 months ago. Direct link to Gonzalo Sandmeier's post “Hello! That's a great obs...” Hello! That's a great observation and method for understanding quadratic equations. The formula you mentioned, Ax^2 + Bx - C = 0, certainly has its benefits. It's a quadratic formula derived from completing the square. The quadratic formula you provided, where A*C = a*b and B = a + b, can be derived by equating the quadratic equation, ax^2 + bx + c = 0, with this particular form. By assuming that the equation has real roots, and then manipulating it further, you'll eventually arrive at the given formula. The advantage of using this form is that it allows you to see the connection between the quadratic equation and the coefficients A, B, and C. For example, you can notice the relationship between A and C and A^2 and C^2. This approach can be helpful for understanding various properties and relationships between the coefficients. In the end, both the traditional quadratic formula (-b ± √(b^2 - 4ac))/(2a) and the form you mentioned are mathematically equivalent. Using either form is a matter of personal preference and what you find most intuitive. It's great that you have found a method that helps you learn and understand quadratic equations better. (3 votes) Altangerel Chinzorig 2 years agoPosted 2 years ago. Direct link to Altangerel Chinzorig's post “Why does it say we cannot...” Why does it say we cannot use grouping on this one 2x^2+3x+4x+12. It is usable though isn't it? Answer would be (x+2)(2x+3) right? • (1 vote) Kim Seidel 2 years agoPosted 2 years ago. Direct link to Kim Seidel's post “Your factors actually don...” Your factors actually don't create the polynomial. If you multiply your factors, you will get: 2x^2+3x+4x+6, which does not match the original polynomial. Now, how do you know if isn't working before checking the factors by multiplying them. Pull the GCF from each pair of terms to get: Notice, the 2 binomials in parentheses do not match. To go to factors from this point, we need to remove a common binomial factor from each term. There is no common binomial factor. This tells use that the polynomial is not factorable. Hope this helps. (11 votes)Want to join the conversation?
6*10 = 60, so we need to find two numbers that add to 19 and multiply to give 60. These numbers (after some trial and error) are 15 and 4. So split up 19x into 15x + 4x (or 4x + 15x), then factor by grouping:
= 3x(2x + 5) + 2(2x + 5)
= (3x + 2)(2x + 5).
It is the value that you can evenly divide all terms by. It can be a number, a variable, or a mix of numbers and variables.
A quadratic is basically a type of problem that deals with a variable multiplied by itself — an operation known as squaring.
So, you could relate the word quadratic to Latin, not mathematics
Take 8 and 6, the factors of those two numbers are 1 and 2.
2 is bigger, so the GCF of 8 and 6 is 2.
That works the same with every other set of numbers.
The factors of 3 are 1,3
The factors of 4 are 1,2,4
Why dont you use the formula Ax^2+Bx-C where A*C=a*b AND B=a+b ? It helps me to learn it this way, since it opens up for future equations that take the square of A and C.
2x^2+3x+4x+12 = x(2x+3) + 4(x+3)
