Question

Ok I got two I need help with :

1. Factor Completely
7x^2 + 49x + 42
I get 7x^2 + 7x + 42x + 42
then 7x(x+1) but the right side is confusing me. I know it should be (x+6).
So the answer is 7x(x+1)(x+6) But I get 7x(x+1) 7(6x+6). What am I doing wrong?


2.Factor completley:
x^10y^3 - 4x^9y^2 - 21x^8y

Totally consfused on this one.

Answer 1

On the first, factor 42 out of the second paren.
7x(x+1)+ 42(x+1)
(x+1)(7x+42)
now factor 7 out of the second..
7(x+1)(x+6)
Onthe last, factor the common factor x^8*y out
yx^8[(xy)^2 -4xy -21]

The last term factors to (xy-7)(xy+3)

Answer 2

Solution for No.1
7x^2 + 49x + 42
7x^2 + 7x + 42x + 42
(7x^2 + 7x) + (42x + 42)
[7x(x+1)+ 42(x+1)]
(7x+42)(x+1)
7(x+6)(x+1)

Solution for No.2
x^10y^3 - 4x^9y^2 - 21x^8y
x^8y (x^2y^2 - 4xy - 21)
x^8y (xy-7)(xy+3)