SOLUTION: I need to Know how to Factor a Quadratic Trinomial when the leading coefficient is not one. The book does not show me how to do it step by step, and I am really confused with how t

Question 70230This question is from textbook Heath ALGEBRA 1 Larson, Kanold, Stiff
: I need to Know how to Factor a Quadratic Trinomial when the leading coefficient is not one. The book does not show me how to do it step by step, and I am really confused with how to go about solving the problem. FOr example, the problem number 33 says: 14x2 - 19x - 40
thank you, MERMAIDMERCY This question is from textbook Heath ALGEBRA 1 Larson, Kanold, Stiff

Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
14X^2-19X-40
YOU NEED TO MAKE A TABLE OF FACTORS FOR THE FIRST & THE LAST TERMS
14*****-40 SUCH THAT THE THE SUMS OF THE PRODUCTS ARE -19 THUS
--------------------
THE FACTORS OF 14 ARE 1*14,-1*-14, 2*7,-2*-7
THE FACTORS OF -40 ARE -1*40,1*-40,2*-20,-2*20,4*-10,-4*10,5*-8,-5*8
STARTING WITHN THE FIRST SET OF FACTORS WE GET
1*-1+14*40=-1+560=559 NOT A SOLUTION
1*40+14*-1=40-14=26 NOT A SOLUTION
2*5+7*-8=10-56=-46
2*-8+7*5=-16+35=19
2*8+7*-5=16-35=-19 THIS IS THE SOLUTION WHEN YOU MULTIPLY THE OUTER NUMBERS & ADD IN THE INNER NUMBERS USING THE FOIL PROCESS THUS:
(2X-5)(7X+8) EXPANDING THIS TERMS WE GET
14X^2-35X+16X-40
14X^2-19X-40

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