College Math Algbrea 2 Help please

Question

completely factor the polynomial 7x^3+35x^2+7x+35=

Answer 1

Hi David;

Arthur just answered an identical question from another resident of Melbourne, FL.  He expressed it his way, I will do such my way.

7x³+35x²+7x+35

First, let's notice the 7 and 35.  We know that 7x5=35.

7(x³+5x²+x+5)

Let's factor the parenthetical equation...

We know that the...

FIRST must be (x²)(x)=x³.

OUTER and INNER must add-up to 5x² and x.

LAST...must be (5)(1) or (1)(5).

7(x²+1)(x+5)

Let's FOIL...

FIRST...(x²)(x)=x³

OUTER...(x²)(5)=5x²

INNER...(1)(x)=1x=x

LAST...(1)(5)=5

7(x³+5x²+x+5)