factoring..need help please?

(6x + 1)(x + 5).

(3x + 5)(2x – 1).

2.) (x+5)(6x+1)

3.) (3x+5)(2x-1)

Remember to F.O.I.L (First, Outside, Inside, Last) to check your answers. For example, take the first question; we’ll work it backwards.

(6x+5)(x+1)

First, multiply the FIRST part of each quantity in parentheses.

(6x)(x)=6x^2

Then, multiply the OUTSIDE numbers in each parentheses.

(6x)(1)=6x

Next, multiply the INSIDE numbers in each parentheses.

(5)(x)=5x

Finally, multiply the LAST numbers in each parentheses.

(5)(1)=5

Then, you add all of those answers that you got from FOILing together.

6x^2 + 6x + 5x + 5

And then simplify.

6x^2 + 11x + 5

Notice that we get the same answer that as the original question. That means that we have the right factors.

You have to guess what the factors are going to be, then you FOIL your guess to see if you’re correct. Don’t be afraid of guessing incorrectly before finally discovering the correct answer. With practice, your guesses will become better and better.

Be careful of negative numbers when you’re FOILing to check your answers. You can tell you’re going to have negative numbers if there’s subtraction in the original question, like your third question. Let’s go through the FOIL process to check my answer for number 3, to make sure I’m correct.

(3x+5)(2x-1)

First: (3x)(2x) = 6x^2

Outside: (3x)(-1)= -3x (note the negative numbers)

Inside: (5)(2x)=10x

Last:(5)(-1)= -5 (again, note the negative numbers)

Now, we add those.

6x^2 + (-3x) + 10x + (-5)

Anytime we’re adding negative numbers, it’s the same as subtracting, so I’ll rewrite the equation to reflect that.

6x^2 – 3x + 10x – 5

Now, we simplify the equation.

6x^2 + 7x – 5

When we FOILed, our answer is the original answer. So, my guess is correct. Again, though, don’t be afraid of guessing wrong a few times.