Question

Solve 15x^3 (x^2 -11x + 30) ÷ 5x^2 (x - 5)
Pls Answer

Answer 1

Answer:

$x$ × (5x-2) × (3x-1)

Step-by-step explanation:

.= Multiply

((15 • (x3)) -  11x2) +  2x

 ((3•5x3) -  11x2) +  2x

Pull out like factors :  

15x3 - 11x2 + 2x  =   x • (15x2 - 11x + 2)

The first term is,  15x2  its coefficient is  15 .

The middle term is,  -11x  its coefficient is  -11 .

The last term, "the constant", is  +2  

Step-1 : Multiply the coefficient of the first term by the constant   15 • 2 = 30  

Step-2 : Find two factors of  30  whose sum equals the coefficient of the middle term, which is   -11 .

     -30    +    -1    =    -31  

     -15    +    -2    =    -17  

     -10    +    -3    =    -13  

     -6    +    -5    =    -11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  -5  

                    15x2 - 6x - 5x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3x • (5x-2)

             Add up the last 2 terms, pulling out common factors :

                    1 • (5x-2)

Step-5 : Add up the four terms of step 4 :

                   (3x-1)  •  (5x-2)

            Which is the desired factorization