///A. | VJT 



and to satisfied for all fmito ralu*s of y ; 



F = 0, and * 0; 



hence, liininatii. K 4, 2 FG - C7/ . 0. 



Hut i. expression to which A reduces when ^ - B-0 



//*.<; h-nr,.. in all oases, A = to the iMcvory condiltou thai the 



iwe quadratic may be factored. 

 That A = u also the u/gffrir n/ condition to readily seen by retracing 

 steps from equation [17] hfii at least one of the coeftcienU i . /. 

 ffers from lero. Hut it it also sufficient when A = B n thai 



se, A =0 becomes:?/ ' // = 0, which may be written j/T.-^Tf 

 i.-l'-i the same ohemmstances equation (1) becomes equation (3) t which 



Substituting ^ ~ for -^- in equal ion (I), it 

 H II - // 



; i-S - 



u esUblishes the sufficiency of the condition for this case also. 



lustrata the use of equation [17]* examine the equation of 

 Art 66: 



2*-*y-3y+9* + 4j + 7 = 0. 



As an illustration of another practical method of factoring a quadratic 

 expression, <* factoring it post. : equation [17] holds, find the 



factors of 



This locos cuts the *-axis at the points (J, 0), (-4, 0) and the y-axfe at 

 , (0, |); hence the two lines are either 



f + f=l and JL + J=1, orUJ=l and JL + f = i ; 

 II * it "" I 



thrr.forr UM Baeton an :th. r 



2* + 3y - 1 and z - 6y - 4, or B* + 6y - 4 and s - 12 y + 4, 

 Inspection shows that they are (3s + 8y - 1) and (x - 6y + 4). 



TAX. AX. OBOM. 8 



