Answer :
factor by grouping
x^2(x-7) + 6(x-7) = 0 [took x^2 out of the first two and a 6 out of the last two]
(x-7)(x^2+6) = 0 [moved (x-7) out to the front]
x = -i sqrt(6) , i sqrt(6) , 7
only one real solution of x = 7
x^2(x-7) + 6(x-7) = 0 [took x^2 out of the first two and a 6 out of the last two]
(x-7)(x^2+6) = 0 [moved (x-7) out to the front]
x = -i sqrt(6) , i sqrt(6) , 7
only one real solution of x = 7
[tex] x^{3} -7 x^{2} +6x-42=0[/tex]
[tex](x-7) [/tex] is a factor since it is a factor of -42 and 7 is a solution for f(x) to equal 0.
[tex](x-7)(a x^{2} +bx+c)=0[/tex]
[tex](x-7)( x^{2} +bx+6)=0[/tex]
[tex]-7 x^{2} +b x^{2} =-7 x^{2} [/tex]
[tex]-7+b=-7[/tex]
[tex]b=0[/tex]
[tex](x-7)( x^{2} +6)=0[/tex]
[tex]x-7=0[/tex]
[tex] x^{2} +6=0[/tex]
[tex]x=7[/tex] (only solution because you can't square root (-6))
[tex](x-7) [/tex] is a factor since it is a factor of -42 and 7 is a solution for f(x) to equal 0.
[tex](x-7)(a x^{2} +bx+c)=0[/tex]
[tex](x-7)( x^{2} +bx+6)=0[/tex]
[tex]-7 x^{2} +b x^{2} =-7 x^{2} [/tex]
[tex]-7+b=-7[/tex]
[tex]b=0[/tex]
[tex](x-7)( x^{2} +6)=0[/tex]
[tex]x-7=0[/tex]
[tex] x^{2} +6=0[/tex]
[tex]x=7[/tex] (only solution because you can't square root (-6))
