So to help with the first one
2 / x = 5
multiply the x on both sides
2 = 5x
divide by 5 to isolate the x
2/5 = x

For the second one
We will use the diamond to help us find the common factor
\ 1 /
\ /
\ /
2 / \ 4
/ 3 \
/ \

1) the product
2) and 4) the two numbers
and 3) is sum

10 is the product and -7 is the sum
so what two numbers (factors of 10)
will equal -7 when added

so we have these numbers that will equal the product of +10 and we will need to find the ones that will equal -7 as the sum
10*1, 2*5, -1*-10, -2*-5
if we add the two numbers we will find respectively
11, 7, -11, -7
As you can see that -2 + -5 = +10 and -2+-5= +10
So we have found the two numbers
now before we factor the expression looks like
( x + a) (x + b)
and when factored looks like
x^2 + (a+b)x + (a*b)
Now we can plug in the numbers and solve to see if -2 and -5 are right
(x + -2) (x + -5)
we will factor it
x^2 +-5x + -2x + 10
x^2 + -7x + 10
so a = -2 and b = -5

Hope this helps :)

5 0

3 years ago