What is the factorization of the trinomial below 3x^3-24x^2+45x

a. 3(x-3)(x+5)

b. 3(x^2-3)(x+5)

c. 3x(x-3)(x-5)

d. 3x(x-3)(x-5)

1st factor is 3x: 
= 3x(x² - 8x + 15) 

2nd & 3rd factors: 
x² - 8x + 15 = 0 
x² - 4x = - 15 + (- 4)² 
x² - 4x = - 15 + 16 
(x - 4)² = 1 
x - 4 = 1 

= x - 4 - 1, = x - 5 
= x - 4 + 1, = x - 3 

3x(x - 5)(x - 3) are the factors. 

Proof: 
= 3x(x - 5)(x - 3) 
= 3x(x² - 5x - 3x + 15) 
= 3x(x² - 8x + 15) 
= 3x³ - 24x² + 45x

You can use the Pythagorean Theorem to find the length of the third side AB (Identified as "x" in the figure attached in the problem), which says that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:

 a² = b²+c²

 As we can see the figure, the triangle does not have an angle of 90°, but it can be divided into two equal parts, leaving two triangles with a right angle. We already have the values of the hypotenuse and a leg in triangle "A" , so we can find the value of the other leg:

 b = √(a²-c²) b = √(10²-4²) b = 9.16

 With these values, we can find the hypotenuse in the triangle "B": x = √b²+c² x = √(9.16)²+(4)² x = 10