00:01
In this problem we are asked to solve the equation x cube plus 8 x squared plus 5x minus 14 equal to 0.
00:29
So how to do it? putting x equal to 1, we have 1 cube plus 8 times 1 square plus 5 times 1 square plus 5 times 1 minus 14 equals this is 8 plus 1 9 this is 5 so 14 minus 14 0 so that means therefore x sorry x minus 1 is a factor normally we we trace this factorization in the from the line term which does not contain any x like one and like here it is 14 so what are the factors of 14 1 2 7 and 14 so we put values 1 to 7 14 plus minus and track whether the polynomial is 0 so then obviously we can i mean we can conclude that a multiple of or a factor of protein putting a factor of 14 the equation becomes zero so obviously our job becomes simpler and we we can conclude that if the x minus 1 or x minus 2 or x minus 7 is a factor then we will have not only real values a solution also will have integer values because ultimately protein, there is a, the factor of protein will come in the roots, set of roots.
02:49
So here, in the first chance, x minus 1 is a factor we can easily conclude.
02:55
In the first chance, putting 1, we got 0, so we are lucky.
02:58
So, x minus 1 is a factor.
03:00
So now we can manipulate this equation.
03:05
Now, x cubed plus 8x square plus 5x.
03:14
Minus 14 this can be written as x cube minus x squared plus 9 x squared minus 9 x and this is 5x so that will be plus 14x minus 14 this equal to 0 this equal to 0 so it can be written okay therefore taking x square common we have x minus 1 taking 9x common we have x minus 1 plus 14 common of x minus 1 equal to 0 so therefore x minus 1 x squared plus 9x plus 14 equal to 0 now this is a quadratic term and we can do the middle term factorization 14 we can multiply 7 into 2 which becomes 14 and 7 plus 2 is 9 so we can write this x minus 1 x squared plus 2x plus 7 x plus 14 equal to 0 or x minus 1 here if we take x common it will become x plus 2 let us rub this and write it once more here taking x common it becomes x plus 2 plus 7 common it becomes x plus 2 equal to 0.
05:16
So it becomes x minus 1, x plus 2, x plus 7, equal to 0...