3x^2+17x+10
*You have to factor completley but I don't know how too.Please help.!
(3x+2 )(x + 5)
Factoring asks this question: what two factors of 10 add to 17 when one is multiplied by three?
Here is how you factor.
Place two sets of parentheses.
( ) ( )
To get 3X^2, we may use ONLY 3X and X. Simple enough? So 3X goes as the first number in the 1st set of parentheses and x goes as the first in the second set, like so.
(3X )(X ).
Next, look at the signs. The only way we can get a + sign at the end and + sign in the middle is to have both signs in the parentheses to be + so we put that in like so.
(3X+ )(X+ ).
Now we look at the last term (10) and the middle one (17). We want to think of a set of numbers that multiply to give 10 and add (with the others values in the parentheses) add to 17. The ONLY factors of 10 are 10*1 and 5*2. There are four combinations you can use; i.e., we can have 10 in the first set of parentheses and 1 in the second or 1 in the first and 10 in the second. Neither of these combinations will work. Do you see why? So we try the second set of numbers (5*2).
We can try 5 in the first set of parentheses and 2 in the second or 2 in the first and 5 in the second. This set will work. I will let you decide which it is. If you don't understand this, and you need to understand so you can do these on your own, please explain in detail what you don't understand about the procedure.
oh ok thanks. - can you help me with this one because it is way harder than the previous one:
5y^8 - 125 and
this one:
a^2 - 2ab - 15b^2
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Certainly! Let's start with the expression 5y^8 - 125.
To factor this completely, we need to recognize it as a difference of squares.
The expression 5y^8 can be written as (y^4)^2 and 125 as (5^3)^2.
Now let's rewrite the expression:
(1) 5y^8 - 125 = (y^4)^2 - (5^3)^2
By applying the difference of squares formula, (a^2 - b^2) = (a + b)(a - b), we can rewrite equation (1) as:
(2) (y^4 - 5^3)(y^4 + 5^3)
Further simplifications can be made by calculating 5^3 to get:
(3) (y^4 - 125)(y^4 + 125)
So, the completely factored form of 5y^8 - 125 is (y^4 - 125)(y^4 + 125).
Now, let's move on to the expression a^2 - 2ab - 15b^2.
To factor this completely, we need to find two binomials that, when multiplied, give us the original expression.
We will look for two numbers that multiply to give -15b^2 and add up to -2ab.
To do this, we need to factor -15b^2. The possible factors are 1 and -15b, -1 and 15b, 3 and -5b, or -3 and 5b.
Among these options, we see that -3 and 5b when multiplied give us -15b^2, and when added, we get -2ab.
So, we can rewrite the expression a^2 - 2ab - 15b^2 as:
(4) (a - 3b)(a + 5b)
Therefore, the completely factored form of a^2 - 2ab - 15b^2 is (a - 3b)(a + 5b).
I hope this helps! Let me know if you have any further questions.