# Factor the polynomial

• Jan 20th 2011, 02:10 PM
Sapphire19
Factor the polynomial
6 3
x + 16X + 64 =

3 3 2 2
This formula: x
+ a = (X+a)(x - ax + a )

• Jan 20th 2011, 02:11 PM
Sapphire19
oops the problem is
x^6 +16x^3_64 and the formula is X^3+a^3= (x^2-ax + a^2)
• Jan 20th 2011, 02:26 PM
Quote:

Originally Posted by Sapphire19
oops the problem is
x^6 +16x^3_64 and the formula is X^3+a^3= (x^2-ax + a^2)

This is a quadratic in $x^3$

$\left(x^3\right)^2+16\left(x^3\right)+64=\left(x^3 +8\right)\left(x^3+8\right)$
• Jan 20th 2011, 02:34 PM
Sapphire19
That's not the right answer. This is regarding homework on mymathlab. If you write the wrong answer it tells you right away if it is wrong. The answer should look exactly like (except with different numbers)
(x+3)^2 (x^2-3x+9)^2

It says "notice that the given polynomial is a perfect square and can be factored by (x+a)^2.
For example, x^6+54x^3+729= (x^3+27)^2. "Now notice that this answer is the sum of 2 cubes. Now you use the formula that I previously posted to get the answer.
Even with this help that mymathlab gives me I still can't manage to complete this question. After literally over 45 minutes of trying I am giving up because i have A LOT of math homework to do and simply cannot spend 45 minutes on one question!
• Jan 20th 2011, 02:41 PM
e^(i*pi)
Archie Meade's factored form is the sum of two cubes

$x^3+8 = x^3+2^3$
• Jan 20th 2011, 06:23 PM
Quote:

Originally Posted by Sapphire19
That's not the right answer. This is regarding homework on mymathlab. If you write the wrong answer it tells you right away if it is wrong. The answer should look exactly like (except with different numbers)
(x+3)^2 (x^2-3x+9)^2

It says "notice that the given polynomial is a perfect square and can be factored by (x+a)^2.
For example, x^6+54x^3+729= (x^3+27)^2. "Now notice that this answer is the sum of 2 cubes. Now you use the formula that I previously posted to get the answer.
Even with this help that mymathlab gives me I still can't manage to complete this question. After literally over 45 minutes of trying I am giving up because i have A LOT of math homework to do and simply cannot spend 45 minutes on one question!

You don't sound like you've got too much patience!

$x^3+2^3=(x+2)\left(x^2-2x+2^2\right)$

Does that help ?
• Jan 20th 2011, 07:07 PM
mirajshah
Related question
Hi MHFers! I've got what's supposed to be a relatively easy problem here... can anyone solve?
$0.00278=p^{4}\times(1-p)^{3}$

Thanks!
• Jan 21st 2011, 03:17 AM
$0.00278=p^{4}\times(1-p)^{3}$