Question

Factor the following trinomials . x2 + 2x - 35 x2 - x - 12

Answer 1

X2-2x-35=0x2-7x+5x-35=0x(x-7)+5(x-7)=0(x-7)(x+5)=0x-7=0      or  x+5=0x=7         or  x=-5 Check: x=7 ,LHS = 49-14-35                          =0 =RHS           x=-5, LHS = 25+10-35                           =0=RHSAns: x=7 or x=-5


x2−x−12=0

Answer 2

(x + 7) • (x - 5)= Answerx^2+2x-35
What multiplies to -35 and adds up to 3?
-5+7=2
-5*7=-35  
NEXT
 x^2 - 5x + 7x - 35

Add up the first 2 terms, pulling out like factors :
                    x • (x-5)

Add up the last 2 terms, pulling out common factors :
                    7 • (x-5)
Add up the four terms of step 4 :
 (x+7)  •  (x-5)

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(x + 3) • (x - 4)=Answer
x^2-x-12
What multiplies up to -12 and adds to -1?
-4+3=-1   
-4*3=-12

Next

x^2 - 4x + 3x - 12

Add up the first 2 terms, pulling out like factors :
                    x • (x-4)

Add up the last 2 terms, pulling out common factors :
                    3 • (x-4)
Add up the four terms
                    (x+3)  •  (x-4)