Sometimes im told to find 2 numbers that add to 6 and multiply to 8 or I need to find the gcf or I need to find number for all the numbers and the varible too? Like how do you know what to do in what problem? Some start with x^2 some start with 8x^2, its confusing.

I think your question is How to factor The quadratic:

X^ 2 + 7 X + 10 =0

always f(x) = ( X +a ) ( X+b ) = X^2 + ( a +b ) X + ab

Roots , the values of X that makes f( x) =0

( X+a ) = 0 X

_{1}= -a ( X+ b) = 0 X_{2 }= -b X^2 + ( a + b) X + ab = X^2 + ( X1 + X2 ) X + X1X2

with a =1

always : X

_{1}+ X_{2 }= - b X

_{1 . }X_{2 = }c X^2 + 7X + 10 =0

- (X

_{1}+ X_{2}) = 7 X_{1 }. X_{2 }= 10 ( 2) 2, 5 are the answer for X1 x2

then :

X^2 + 7X + 10 = ( X +2 ) ( X +5 ) =0 X = -2 X = -5

If System of equation( 2 ) doesn't have integer solution, then we have to factor by completing

the square.

for a ≠ 1

i.e.

2 X^2 + 7X +5 = 0 then -( X

_{1 }+ X_{2 )= 7/2 }X_{1 }. X_{2 = ( 5 /2)} again answer X

_{1}= -1 X_{2}=- 5/2 To factor we break 7 into 2 +5

2 X^2 + 2X + 5X + 5=0

Factoring by grouping :

2X ( X + 1 ) + 5 ( X +1 ) = 0

( X +1 ) ( 2X + 5) =0

X = -1 X = -5/2