# SOLUTION: Factor:72+22x-x²

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Factor:72+22x-x²      Log On

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 Question 418019: Factor:72+22x-x²Found 2 solutions by shree840, Edwin McCravy:Answer by shree840(260)   (Show Source): You can put this solution on YOUR website!Use the formula. no factoring is possible. Answer by Edwin McCravy(9716)   (Show Source): You can put this solution on YOUR website!``` 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". --------------------------------------------- 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```