Does "2x to the fourth power, minus 32" factor any lower than 2(x to the fourth power, minus 16) ??
2007-05-08 06:34:33 · 6 answers · asked by John Paul Jones 2 in Science & Mathematics ➔ Mathematics
Hi,
2x^4 - 32
Take out the GCF of 2.
2(x^4 - 16)
The binomial is the difference of perfect squares and factors into:
2(x^2 - 4)(x^2 + 4)
The factor with a minus is still the difference of perfect squares so it factors again. The others stay the same.
2(x - 2)(x + 2)(x^2 + 4)
these are your factors, which can be listed in any order.
I hope that helps!! :-)
2007-05-08 06:41:04 · answer #1 · answered by Pi R Squared 7 · 0⤊ 0⤋
You bet it does!
2x^4 - 32 = 2(x^4 - 16) = 2(x^2 + 4)(x^2 - 4) = 2(x^2 + 4)(x + 2)(x - 2)
Remember: a^2 - b^2 = (a + b)(a - b)
2007-05-08 13:43:37 · answer #2 · answered by airtime 3 · 0⤊ 0⤋
2x^4 - 32
2(x^4-16)
Now, x^4 and 16 are both perfect squares, so you have the difference of squares.
2[(x^2-4)(x^2+4)]
If you wanted, x^2-4 is also a perfect square, so you have the difference of squares again.
2[(x-2)(x+2)(x^2+4)]
2007-05-08 13:54:43 · answer #3 · answered by danjlil_43515 4 · 0⤊ 0⤋
2(x^2+4)(x^2-4)
2007-05-08 13:45:36 · answer #4 · answered by mago 5 · 0⤊ 0⤋
2 x^4-32
2(x^4-16)
2(x^2-4)(x^2+4)
2(x-2)(x+2)(x^2+4)
2007-05-08 14:50:35 · answer #5 · answered by Dave aka Spider Monkey 7 · 0⤊ 0⤋
Do a couple of square roots.
2007-05-08 13:44:08 · answer #6 · answered by Richard F 7 · 0⤊ 0⤋