x ^ 3 - 4 x ^ 2 - 25 x + 100 =
( x ^ 3 - 4 x ^ 2 ) + ( - 25 x + 100 ) =
( x ^ 3 - 4 x ^ 2 ) - ( 25 x - 100 ) =
x ^ 2 ( x - 4 ) - 25 ( x - 4 ) =
( x - 4 ) ( x ^ 2 - 25 ) =
( x - 4 ) ( x + 5 ) ( x - 5 )
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Remark :
a ^ 2 - b ^ 2 = ( a + b ) ( a - b )
So :
x ^ 2 - 25 = x ^ 2 - 5 ^ 2 = ( x + 5 ) ( x - 5 )
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y = ( x - 4 ) ( x + 5 ) ( x - 5 ) = 0
x - 4 = 0
x = 4
x + 5 = 0
x = - 5
x - 5 = 0
x = 5
The solutions are :
x = - 5
x = 4
and
x = 5
I really need help on this. I tried doing it on my own, but, I got stuck. Thanks!
(a) List any approximate x-intercepts values.
(b) Set y = 0 and solve the resulting equation; y=x^3-4x^2-25x+100.
3 answers
الهندسة
Not much engineering here. Must have been a test post.