Question

Ricardo is factoring the polynomial, which has four terms. 5x3 + 20x2 + 2x + 8 5x2(x + 4) + 2(x + 4) Which is the completely factored form of his polynomial?

A. 5x2(x + 4)
B. 7x2 (x + 4)
C. (7x2 + 2) (x + 4)
D. (5x2 + 2) (x + 4)

Answer 1

5x^3+20x^2+2x+8

5x^2(x+4)+2(x+4)

(5x^2+2)(x+4)

Answer 2

Option D is correct

Explanation:

Ricardo is factoring the polynomial which has four terms.

`5x^3+20x^2+2x+8`.

Factor by grouping,

`5x^2(x + 4)+2(x + 4)`

If all of the terms in a polynomial contain one or more identical factors, combine those similar factor into one monomial, called Greatest Common Divisor(GCD).

In polynomial i.e
`5x^2(x + 4)+2(x + 4)` there is factor (x+4) that's greatest common divisor.

Finally, writing factored expression as the product of the GCD and the remaining terms,

`(x + 4) \cdot \left ( 5x^2+2 \right )`

Therefore, Completely Factored form of his polynomial is,
`(x + 4) \cdot \left ( 5x^2+2 \right )`