SOLUTION: I need confirmation on this problem involving factoring: Factor Completely: 16x^4 - 40x^2 + 9 = This is what I came up with: 8(2x^4

SOLUTION: I need confirmation on this problem involving factoring: Factor Completely: 16x^4 - 40x^2 + 9 = This is what I came up with: 8(2x^4 - 5x^2) + 1 is this correct? Thanks for

Question 173654: I need confirmation on this problem involving factoring:
Factor Completely: 16x^4 - 40x^2 + 9 =
This is what I came up with:
8(2x^4 - 5x^2) + 1 is this correct? Thanks for any assistance.
Found 2 solutions by nerdybill, Fombitz:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
16x^4 - 40x^2 + 9 =
This is what I came up with:
8(2x^4 - 5x^2) + 1 is this correct?
.
No
if you expanded your equation:
8(2x^4 - 5x^2) + 1
You would get:
16x^4 - 40x^2 + 1
Which is NOT the same as what you started with.
.
The correct solution is:
16x^4 - 40x^2 + 9
(4x^2-1)(4x^2-9)
.
Can't stop here either because it can be further factored:
(4x^2-1)(4x^2-9)
(2x+1)(2x-1)(2x-3)(2x+3)
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
No that's not correct.
Let's expand what you got.

Let's try this.
Use a substitution to knock down the degree of the polynomial and hopefully make it look more familiar.
Let
Now substitute this into your equation.

Now you have a quadratic equation in u and you can look to factor the right hand side,

You can further factor the right hand sides,

.
.
.

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