Pascha is factoring the polynomial, which has four terms.
3x3 – 15x2 + 8x – 40
3x2(x – 5) + 8(x – 5)
which is the completely factored form of her polynomial?
(3x2 – 5) (x + 8)
(3x2 – 8) (x + 5)
(3x2 + 8) (x – 5)
(3x2 + 5) (x – 8)

Option (c) is correct.

The complete factored form of her polynomial is

Step-by-step explanation:

Given :  Pascha is factoring the polynomial, which has four terms.

is factored as  

We are required to choose the completely factored form of her polynomial from the given options.

Factored form of a polynomial is writing the polynomial in the smallest form so that when we multiply we get the same original  polynomial.

Consider

Taking (x-5) common from both terms , we get,

Thus, we obtained

Hence, option (c) is correct.

The complete factored form of her polynomial is

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

step-by-step explanation: