So we go right into factoring the trinomial of the form
(x
)(x
)
Putting that into our factors we get:
We need to factor out the GCF,
as shown in Tutorial 27: The GCF and Factoring by Grouping,
first before we tackle the trinomial part of this.
In the second terms of the binomials, we need factors of -1. This would have to be 1 and -1.
Also, we need to make sure that we get the right combination of these
factors.
Possible Factors
Check using the FOIL
method Tutorial 26 (Multiplying
Polynomials)
First try:
This is our original polynomial.
So this is the correct combination of factors for this polynomial.
Since x is already being used in this problem,
let's use y for our substitution.
*Substitute y in
for x squared
In the second terms of the binomials we need factors of -20. This would have to be -5 and 4, 5 and -4, -2 and 10, 2 and -10, 20 and -1, or -20 and 1 .
Also we need to make sure that we get the right combination of these
factors.
Possible Factors
Check using the FOIL
method Tutorial 26 (Multiplying
Polynomials)
First try:
This is our original polynomial.
So this is the correct combination of factors for this polynomial.
(x
)(x )
Can you think of any????
Since the product is a positive number and the sum is a negative number, we only need to consider pairs of numbers where both signs are negative.
One pair of factors of 10 is -10 and -1, which does not add up to
be -4.
Another pair of factors are -2 and -5, which also does not add up
to -4.
Since we have looked at ALL the possible factors, and none of them
worked, we can say that this polynomial is prime.
In other words, it does not factor.
Last revised on July 15, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward.
All rights reserved.