Multiply.

(x2 – 5x)(2x2 + x – 3)

A.
2x4 – 9x3 – 8x2 + 15x

B.
2x4 – 9x3 – 9x2 – 15x

C.
4x4 + 9x3 – 8x2 + 15x

D.
2x4 + 9x3 – 8x2 + 15x

x • (x - 5) • (x - 1) • (2x + 3)

Step-by-step explanation:

((x2) -  5x) • ((2x2 +  x) -  3)

Pulling out like terms :

3.1     Pull out like factors :

  x2 - 5x  =   x • (x - 5)

Trying to factor by splitting the middle term

3.2     Factoring  2x2 + x - 3

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +x  its coefficient is  1 .

The last term, "the constant", is  -3

Multiply the coefficient of the first term by the constant   2 • -3 = -6

Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   1 .

     -6    +    1    =    -5

     -3    +    2    =    -1

     -2    +    3    =    1    That's it

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

                    2x2 - 2x + 3x - 3

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

                   2x • (x-1)

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

                   3 • (x-1)

Add up the four terms of step 4 :

                   (2x+3)  •  (x-1)

            Which is the desired factorization

Final result :

 x • (x - 5) • (x - 1) • (2x + 3)

Processing ends successfully

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step-by-step explanation: