What is the simplified form of the quantity 4 x squared minus 25 over the quantity 2x minus 5 ?

a 2x − 5, with the restriction x ≠ −five over 2

b 2x + 5, with the restriction x ≠ five over 2

c 2x − 5, with the restriction x ≠ five over 2

d 2x + 5, with the restriction x ≠ −five over 2

  B.  2x + 5, with the restriction x ≠ five over 2

Step-by-step explanation:

The given expression is the difference of squares, so factors as ...

  the product of the quantity 2x plus 5 and the quantity 2x minus 5 over the quantity 2x minus 5

You will note that the numerator and denominator have a common factor:

  the quantity 2x minus 5

Factoring that out gives ...

  2x + 5, with the restriction x ≠ five over 2 (x is restricted from being a value that makes the denominator zero.)

Comment on the form of the answer

Since you have written your math expressions using words instead of symbols, we assume you can read them more easily that way. So, we have provided the explanation in the form you can most easily understand. (Personally, I prefer math symbols. They are more compact and tend to be less ambiguous.)

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.