Question

factor completely 4x5 − 20x4 − 36x3. 4(x5 − 5x4 − 9x3) x3(4x2 − 20x − 36) x2 − 5x − 9 4x3(x2 − 5x − 9)

Answer 1

Answer: 4x^3( x^2 - 5x - 9)

Proof of validity is shown below.

Answer 2

Consider the polynomial
`4x^5 - 20x^4 - 36x^3.` It has three terms and their greatest common factor is
`4x^3.`

Since

`4x^5=4x^3\cdot x^2,\\20x^4=4x^3\cdot 5x,\\36x^3=4x^3\cdot 9,`

then

`4x^5 - 20x^4 - 36x^3=4x^3(x^2-5x-9)` (you write in brackets the same sign as the corresponding term has).

Answer: correct choice is D.