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8) Factor x^2 + 6x - 40
\n" ); document.write( " Ans:
\n" ); document.write( " Given equation is x^2+6x-40.
\n" ); document.write( " (To find the factor for this type of equation first we see that there is any coefficient in the high factor)
\n" ); document.write( " Here no coefficient with high power.
\n" ); document.write( " So first we consider the constant i.e.,-40.
\n" ); document.write( " Next we split this constant into mutliple of two variables also we note that the addition of two variables gives the coefficient of second higher power.
\n" ); document.write( " Therefore, -40 = 10 x -4 (10-4=+6)
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\n" ); document.write( " Now the given equation can be written as
\n" ); document.write( " x^2+10x-4x-40 = 0
\n" ); document.write( " x(x+10)-4(x+10)=0
\n" ); document.write( " (x+10)(x-4)=0
\n" ); document.write( " x=-10 and x=4
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\n" ); document.write( " Thus the factor x=-10,4.
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\n" ); document.write( "\n" ); document.write( "9) Factor 3x^2 + 2x – 5
\n" ); document.write( " Ans:
\n" ); document.write( " Given equation is 3x^2+2x-5=0.
\n" ); document.write( " Here there is coefficient with high power (x^2).
\n" ); document.write( " So that coefficient is mutliply with the constant.
\n" ); document.write( " i.e., 3x(-5)= -15
\n" ); document.write( " -15 = 5 x-3 = 2(second high power coefficient)
\n" ); document.write( " Now the given equation can be written as
\n" ); document.write( " 3x^2-3x+5x-5=0
\n" ); document.write( " 3x(x-1) +5(x-1)=0
\n" ); document.write( " (3x+5)(x-1)=0
\n" ); document.write( " 3x+5=0 and x-1=0
\n" ); document.write( " 3x=-5 and x=1
\n" ); document.write( " x=-5/3 and x=1\r
\n" ); document.write( "\n" ); document.write( " Thus the factor of the given equation is
\n" ); document.write( " x = -5/3, 1 \n" ); document.write( "