Factoring Help?

Question

I need someone to give me step by step instructions on how to solve a problem like this. Please, give the step by step instructions as if I had no clue how to do math at all. Thanks!

Factor: p^2 + 5p + 10

Answer 1

Since the coefficient of p^2 is 1, you're getting off easy. If the coefficient of p^2 is not 1, divide the whole equation by the coefficient and proceed to the next step. List all the factors of the constant term (10) in pairs that multiply to the term. In this case, you have 10 and 1, 5 and 2. Be sure you have all the factor pairs. Check if any of the pairs add to or subtract to the first degree term (5). In this example, 10 + 1 is 11, 10 - 1 is 9, 5 + 2 is 7, and 5 - 2 is 3. You are out of luck here-- none of them add or subtract to 5, your first degree term. This one is not to be factored, except possibly with fractions or imaginary numbers, in this case imaginary numbers, and I doubt you'd get one of those on a test.

Let's try another example: p^2 + p + 6. The factors of 6 are 6 and 1, 3 and 2. 6 + 1 is 7. 6 - 1 is 5. 3 + 2 is 5. 3 - 2 is 1. The pair 3 and 2 subtract to 1, your first degree term. If they add to this term, both are positive in the factored form, but if they subtract to this term, one is negative and it doesn't matter which. Your answer takes the form (p + one factor) * (p + other factor). In this case, (p + 2) * (p - 3) = p^2 + p + 6, or (p + 3) * (p - 2).

Good luck!

Answer 2

Let's try factoring by completing the square:
p^2 + 5p + 10 =
p^2 + 5p + (5/2)^2 + 10 - (5/2)^2 =
(p + 5/2)^2 + 10 - 25/4 =
(p + 5/2)^2 + (40 - 25)/4 =
(p + 5/2)^2 + 15/4 =
(p + 5/2)^2 - (- 15/4)
which is a difference of squares of sorts., but the quantity in parenthesis is negative.
(p + 5/2)^2 - (- 15/4) =
(p + 5/2 - √(- 15/4))(p + 5/2 + √(- 15/4))
Using i = √-1.
(p + 5/2 - √(- 15/4))(p + 5/2 + √(- 15/4)) =
(p + 5/2 - i(1/2)√15)(p + 5/2 + i(1/2)√15)

Answer 3

It's not factorable.
The factors of 10 are 10 and 1 or 5 and 2. Neither pair add up to 5, the middle term.

Answer 4

p^2 + 5p + 10

so
(p ) (p )
now two numbers that multply to give + 10 and add to give 5
erm.....
( p + ) ( p + )

ah wait...
b^2-4ac = 25-4*1*10 = -15
since it's <0 it has no roots and isn't factorisable.

Answer 5

what