Question

Which product of prime polynomials is equivalent to 30x3 – 5x2 – 60x?

Answer is C 5x(2x – 3)(3x + 4) in e2020

Answer 1

Answer: 5x(2x-3)(3x+4)

Explanation:

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Answer 2

Since
`30x^3-5x^2-60x=5x(6x^2-x-12)`, you have to find factors of polynomial
`6x^2-x-12`.

For the polynomial
`6x^2-x-12`


`D=(-1)^2-4\cdot6\cdot (-12)=1+288=289 \\ √(D)= √(289) =17 \\ x_(12)= (-(-1)\pm 17)/(2\cdot 6)`.


`x_1= (1+17)/(12)= (18)/(12) = (3)/(2) \\ x_1= (1-17)/(12)=-(16)/(12) =- (4)/(3)`
and

`6x^2-x-12=6(x- (3)/(2) )(x- (-(4)/(3)) )=(2x-3)(3x+4)`.
Then
`30x^3 - 5x^2 - 60x=5x(6x^2-x-12)=5x(2x-3)(3x+4)`.