Math algebra homework factoring

There are many more possible ways to factor 12, but these are representative of many of them. A common method of factoring numbers is to completely factor the number into positive prime factors. A prime number is a number whose only positive factors are 1 and itself. For example, 2, 3, 5, and 7 are all examples of prime numbers.

Okay since the first term is x 2 x 2 we know that the factoring must take the form. We know that it will take this form because when we multiply the two linear terms the first term must be x 2 x 2 and the only way to get that to show up is to multiply x x by x x. Therefore, the first term in each factor must be an x x.

It is easy to get in a hurry and forget to add a “+1” or “-1” as required when factoring out a complete term. This one looks a little odd in comparison to the others. However, it works the same way. There is a 3 x x in each term and there is also a 2 x + 7 2 x + 7 in each term and so that can also be factored out.

Example: factor 3y 2 +12y. Firstly, 3 and 12 have a common factor of 3. So we could have: 3y 2 +12y = 3(y 2 +4y) But we can do better! 3y 2 and 12y also share the variable y. Together that makes 3y: 3y 2 is 3y × y; 12y is 3y × 4 . So we can factor the whole expression into: 3y 2 +12y = 3y(y+4) Check: 3y(y+4) = 3y × y + 3y × 4 = 3y 2 +12y