i am having a hard time with factoring i have read what is here but am still having trouble can some one help me with the problem s^2-s-6, and y^2-4y-5. these are expressions which either can be factored or are prime. can someone explain how to do these in regular terms.

Of course! I'd be happy to help you with factoring these expressions.

Let's start with the expression s^2 - s - 6:

1. Look for two numbers that multiply to give the constant term (-6) and add up to give the coefficient of the middle term (-1).
In this case, the numbers are -3 and 2 since (-3) * 2 = -6 and (-3) + 2 = -1.

2. Rewrite the middle term (-s) using these two numbers.
s^2 - 3s + 2s - 6

3. Group the terms and factor by grouping:
(s^2 - 3s) + (2s - 6)
s(s - 3) + 2(s - 3)

4. Notice that both groups have a common factor of (s - 3):
(s - 3)(s + 2)

So the factored form of s^2 - s - 6 is (s - 3)(s + 2).

Now let's move on to the expression y^2 - 4y - 5:

1. Look for two numbers that multiply to give the constant term (-5) and add up to give the coefficient of the middle term (-4).
In this case, the numbers are -5 and 1 since (-5) * 1 = -5 and (-5) + 1 = -4.

2. Rewrite the middle term (-4y) using these two numbers.
y^2 - 5y + y - 5

3. Group the terms and factor by grouping:
(y^2 - 5y) + (y - 5)
y(y - 5) + 1(y - 5)

4. Notice that both groups have a common factor of (y - 5):
(y - 5)(y + 1)

So the factored form of y^2 - 4y - 5 is (y - 5)(y + 1).

I hope this explanation helps you understand the process of factoring these expressions. Let me know if you have any further questions!

Of course! Factoring can be tricky at first, but with some practice, you'll become more comfortable with it. Let's break down the process for factoring the given expressions.

Expression 1: s^2 - s - 6

To factor this expression, we need to find two binomials that, when multiplied together, give us the original expression s^2 - s - 6.

First, we look for two numbers that multiply to give -6 and add to give -1 (the coefficient of the middle term, -s). The numbers that meet these criteria are -3 and +2.

Now, we can rewrite the expression as follows:

s^2 - s - 6 = (s - 3)(s + 2)

Here, we have factored the expression s^2 - s - 6 into two binomials: (s - 3) and (s + 2).

Expression 2: y^2 - 4y - 5

Similarly, we need to find two binomials that multiply to give us y^2 - 4y - 5.

In this case, we are looking for two numbers that multiply to give -5 and add to give -4 (the coefficient of the middle term, -4y). The numbers that satisfy these conditions are -5 and +1.

Now, we can rewrite the expression as follows:

y^2 - 4y - 5 = (y - 5)(y + 1)

Here, we have factored the expression y^2 - 4y - 5 into (y - 5) and (y + 1), two binomials.

By following this method, you can factor expressions by identifying the appropriate numbers that satisfy the multiplication and addition requirements. It may take some practice to get comfortable with factoring, so don't hesitate to keep trying with different examples.

They factor into (s-3)(s+2) and

(y-5)(y+1)

Look at the constant term at the end and see what prime number it can be factored into. In the case of 6 (in the first problem), it can be either 3 and 2, or 6 and 1. Because of the minus sign in front of the 6, you have to have opposite signs on the two numbers that you pick. Also, the sum of the two must be -1 (the coefficient of the middle "s" term). The numbers that meet these requirements are -3 and +2. Hence the factors are (s-3) and (s+2)

If the coefficent of the "square" term were not 1, the problem gets a bit more complex, but it still comes down to looking for prime number factors of the squared term's coefficient and the constant term, computing the middle term, and a bit of trial and error.

s^2 - s - 6

What you're looking for is a number that when you multiply it, it equals
-6 and when you add them it equals -1. these values -6 and -1 are derived from the equation.

so number could be --> -/+ 3, -/+ 2
but since there's only one way of getting -1 when you add them. the answer is -3 and 2.

when you multiply -3 and 2==> -6
when you add them it equal ==> -1

so ==> ans= (s-3)(s+2)

Try to do the same for the other problem.