Hello there! I can help you! Both problems are set up in the form of ax^2 + bx + c. What we will do for both is multiply a and c together, and find a group of values that add up to b. Let's get started.
1. Okay. 2 is the value of a and 6 is the value of c. -x (-1x) is the value. 2 * 6 is 12. We will find a pair of factors that have a product of 12 and a sum of -1. When we think about it enough, 3 and 4 are factors of 12, but in order to make it into -1, we put the negative symbol infront of the 4. The pair of factors are 3, -4. That makes it (x + 3)(x - 4). However, we are not done yet. We will do something called slide and divide. This means that we will divide the constants by the a value (2), and if they don't divide evenly, we slide it towards the x. 3 and 2 do not divide evenly, so that part becomes 2x + 3. However, 4 can divide into 2 times. In this case, we will not slide it over. It becomes x - 2. There. The expression in factored form is (2x + 3)(x - 2)
2. For this expression, we will do the same steps as expressed above. Multiply a and c, find the factors that have the product of ac AND have a sum of the value of b. 2 * 1 is 2. -7 has to be the sum of the two factors. This can't be put in factored form, because you can't have a number be a product of 2, and have a sum of -7. That's impossible. The expression is already in simplest form.
