I have this worksheet, it has a bunch of different kinds of questions, but i know all the stuff we learned, i just don't know which ones i use. 1) factor each expression, 8x+10 2) Use Foil to factor each expression, x2-5x+6 3) Use foil to factor each expression, n2+n-20.

8 x + 10

all you can do here is factor out 2
= 2 (4x+5)

x^2 - 5 x + 6
is quadratic and of form a x^2 + b x + c
we know it will have factors of form ( p x + q)(r x + s) which we can foil to get the original back (We do not know however if all those constants are integers, but we can hope
Now 6 is either 6*1 or it is 2 * 3
we know p and r are one to get 1 x^2
we know both q and s must be - to get a positive outer product and negative inner product so
so try to FOIL
(x-2)(x-3) (by the way it works)

n^2 + n - 20
well, 20 = 2 * 10 or 20*1 or 4*5
I know I need
(n - something ) (n + something that is one bigger and gives an outer product of 20
so try to FOIL
(n-4)(n+5)

To factor each of these expressions, you can follow specific steps and techniques. Let's take a look at each question and explain how to factor the given expressions:

1) To factor the expression 8x + 10, you need to find the common factor. In this case, you can factor out the greatest common factor, which is 2. Divide each term by 2:
8x / 2 + 10 / 2 = 4x + 5

The factored form of the expression 8x + 10 is 2(4x + 5).

2) To use the FOIL method to factor the expression x^2 - 5x + 6, you want to break down the middle term (-5x) into two terms whose coefficients multiply to give you the constant term (6) and then combine them to fit the FOIL method.

The constant term 6 can only be broken down as follows: 1 * 6 or -1 * -6.

We need to find two values that, when multiplied, give 6, and when added, give -5. The values -2 and -3 satisfy these conditions. So, we can rewrite -5x as -2x - 3x:

x^2 - 2x - 3x + 6

Now, we can group the terms and factor by grouping:
(x^2 - 2x) + (-3x + 6)

Now, factor out the greatest common factor from each group:
x(x - 2) - 3(x - 2)

Notice that (x - 2) appears in both terms. Factor it out:
(x - 2)(x - 3)

The factored form of the expression x^2 - 5x + 6 is (x - 2)(x - 3).

3) Similarly, let's factor the expression n^2 + n - 20 using the FOIL method:

To factor the constant term -20, we want to find two values that, when multiplied, give -20, and when added, give +1 (the coefficient of n).

The values are +5 and -4, as 5 * -4 = -20 and 5 + (-4) = 1.

We can now rewrite the expression:
n^2 + 5n - 4n - 20

Now, group the terms and factor by grouping:
(n^2 + 5n) + (-4n - 20)

Factor out the greatest common factor from each group:
n(n + 5) - 4(n + 5)

You can factor out (n + 5) as it appears in both terms:
(n + 5)(n - 4)

The factored form of the expression n^2 + n - 20 is (n + 5)(n - 4).

By following these step-by-step explanations, you should now be able to factor each of the given expressions on your worksheet.