factorize x squared -8x+15=0?

Answer 1

x ² - 8 x + 15 = 0
( x - 5 ) ( x - 3 ) = 0
x = 3 , x = 5

Answer 2

x² -8x +15 = 0

this is in the form ax² + bx + c = 0.

You need to multiply the 'a' term with the 'c' term. Such that the factors of a*c.. when added give you the middle term. Scary definition. But it's easier in practice.

now a = 1, and c = 15.

a* c = 1 * 15 = 15

Now i need to find the FACTORs of 15.

1 * 15 = 15
3 * 5 = 15

No other factors remain. Now I need to add up the factors of 15 which will give me the middle 'b' term. The 3 + 5 give me the 8. SO these are the numbers i am going to use.

We now need to rewrite the original equation:

x² -8x +15 = 0

becomes..

x² -3x - 5x +15 = 0

** Did you see how i used the 3 and the 5, and made them negative because the b term is negative, and the only way to get -8 would be to mins -5 from a -3?**

x² -3x - 5x +15 = 0


Now we are going to group it.

(x² -3x) - (5x +15) = 0

When we subtract to groups of ploynomials we are supposed to change the negative sign in between them to a positive, and change the sign of everything after that sign to the opposite sign.

(x² -3x) - (5x +15) = 0 --> becomes -- > (x² -3x) + (-5x -15) = 0
We are going to take out what is common from the first group.. I can take out an x from the first group.

(x² -3x) + (-5x -15) = 0

becomes..

x(x -3) + (-5x -15) = 0

We are now going to do the same thing to the second group.
I can take out a 5 from each term in the second group.

x(x -3) + (-5x -15) = 0

becomes ..

x(x -3) -5 (x -3) = 0

Becaome the (x-3) matches, we are going to use it 1 time.

We take the outside terms, and put them into a group of their own..

(x-5)(x-3) = 0

Is the factored form of x² -8x +15 = 0


Hope this helps,

Good luck!

Answer 3

YWCRZ gave you the explaination to do any type of quadratic factoring. BRAVO!

When the coefficient with the squared variable is one you can take a short cut and just look at the "c" value when the equation is in standard form [ ax^2 +bx+c=0]. In your example you are looking for two numbers when combined give you +15. Think of the factors of 15.

1 and 15
3 and 5

The second sign when it is a + means the signs in the parentheses are the same sign.
When the second sign is a (-) you will need one of each sign.
In your case you have a + so you have the same sign in each parentheses.

The first sign tells you what you are looking for. Since the second sign is a - you need both parentheses to be -.

(x- )(x - )=0

Now look at your factors. Which ones when combined give you 8? 5 and 3 right?

(x-5)(x-3)=0 it does not matter which set of parentheses comes first.

If you want to solve it then,

(x-5) =0 ------or-------(x-3)=0
x=5--------or --------------- x=3

Answer 4

x²-8x+15=0
(x-5)(x-3)=0 that is factored if you also want it solved
x=5,3

Answer 5

x^2-8x+15
(x-3)(x-5)

Answer 6

(x-3)(x-5)