Name
Alg1
June 7, 2016
Factoring with x4
x4 + 5x2 – 24
Factor:
1)
2)
3)
Look for a GCF:
a.
There is no GCF for this trinomial
b.
The only way this method works is if you take out the GCF (if there is one.)
Take the coefficient for x2 (1) and multiply it with the last term (24):
x4 + 5x2 – 24
1·24 = 24
x4 + 8x2 – 3x2 – 24
* Now find factors of 24 with a sum of +5. The numbers will
be +8 and -3, which become 8x and 3x. The terms must be
+8x and -3x (because they have a sum of +5x)
SPLIT THE MIDDLE and reduce each side:
x4 + 8x2 | – 3x2 – 24
Take Out: x and -8
x2 (x2 + 8) - 3(x2 + 8)
*When you’re done the binomial on each side
should be the same.
4) Take out the common binomial (x2 + 8) as a GCF, and you are left with x2 on the left and – 3 on the
right. They make up the binomial (x2 – 3)
5)
Your binomial factors are (x2 + 8) and (x2 - 3)
6) Check: (x2 + 8)(x2 – 3)
x2 (x2 - 3) + 8(x2 – 3)
x4 – 3x2 + 8x2 – 24
x4 + 5x2 – 24 (It checks!!)
1) x4 + 13x2 + 22
2) x4 – 5x2 – 66
3) x4 + x2 – 156
4) x4 – 25x2 + 24
Name
Alg1
June 7, 2016
Factoring with x4
5) x4 – 12x2 + 27
6) x4 – 25
7) 9x4 – 16
8) 121x4 – 4
9) x4 – 81
10) x4 – 1
Name
Alg1
June 7, 2016
Factoring with x4
11) x4 – 13x2 + 36
12) x4 – 17x2 + 16
13) x4 + 3x2 – 4
14) 81x4 - 1