Which of the following is a factor of 5x3 − 135? a) 5 b) x + 3 c) x2 − 3x + 9 d) all of the above

The correct answer option is A) 5.

Explanation:

We are given the following expression and we are to factorize it:

If we take the common term out of this, then we are left with:

Now the term can also be written in the form of as:

Next, we will factorize it applying the difference of cubes formula to get:

Adding the common term back to it to get:

Therefore, from the given answer options we can see that the option A) 5 is the factor of the given expression 5x^3 - 135.

answer: hey there,

the answer you are looking for is a..

hope this you!

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240