The other tutor is right in that it does not factor. But
the quadratic formula can only be used to solve an equation.
This is not an equation, but an expression, specifically a
quadratic trinomial, not an equation. Let's see why it
doesn't factor. Let's try anyway:
72+22x-x²
We write it in descending order:
-x²+22x+72
Factor out -1
-1(x²-22x-72)
We look for factor pairs of the last term in
absolute value, 72
72*1=72
36*2=72
24*3=72
18*4=72
12*6=72
9*8=72
Since the sign of the last term is -,
out beside them we SUBTRACT them.
72*1=72 72-1=71
36*2=72 36-2=34
24*3=72 24-3=21
18*4=72 18-4=14
12*6=72 12-6= 6
9*8=72 9-8= 1
We do not find the middle term's coefficient in
absolute value, 22, among those differences.
Therefore the trinomial does not factor.
It is what is called "a prime polynomial".
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If the trinomial had been this instead
-72+22x-x²
it would have factored.
We write it in descending order:
-x²+22x-72
Factor out -1
-1(x²-22x+72)
We look for factor pairs of the last term in
absolute value, 72
72*1=72
36*2=72
24*3=72
18*4=72
12*6=72
9*8=72
Since the sign of the last term is +,
out beside them we ADD them.
72*1=72 72+1=74
36*2=72 36+2=38
24*3=72 24+3=27
18*4=72 18+4=22
12*6=72 12+6=18
9*8=72 9-8= 1
For this problem, We do find the middle term's
coefficient in absolute value, 22, among those differences,
as indicated in red. So we know that we can use the factor
pair 18 and 4.
Therefore we write:
-1(x 18)(x 4)
Next we must fill in signs in the middle of each
parentheses. Since the sign of the middle term
-22 is -, and since 18 is larger than 4, we place
this sign before the larger, which is 18.
-1(x - 18)(x 4)
Since the sign of the last term is -, we place
the opposite sign + before the 4
-1(x - 18)(x + 4)
So the expression you gave, 72+22x-x²
does not factor, but -72+22x-x² does.
72+22x+x² would have factored as (x+18)(x+4)
72-22x+x² would have factored as (x-18)(x-4)
Could a sign have been inadvertently typed wrong?
Edwin
