Answer
$x=${$1/3,1/2,1$}
Work Step by Step
As we can see on the table, the solution to the equation $6x^3-11x^2+6x-1=0$ is $1$.
using synthetic division,
$\begin{array}{lllll}
\underline{1}| & 6 & -11 & 6 &-1 \\
& & 6&-5 & 1\\
\hline & & & & \\
& 6 & -5 & 1 & 0
\end{array}$
$(6x^{3}-11x^2+6x-1)\div(x-1)=6x^2-5x+1$.
we can solve for the quadtratic equation by grouping using the following steps,
1.With the quadratic in standard form, ax2+bx+c=0, multiply a⋅c
2.Find two numbers whose product equals ac and whose sum equals b
3.Rewrite the equation replacing the bx term with two terms using the numbers found in step1 as coefficients of x
4.Factor the first two terms and then factor the last two terms. The expressions in parentheses must be exactly the same to use grouping.
5.Factor out the expression in parentheses.
6.Set the expressions equal to zero and solve for the variable.
$6x^2-3x-2x+1= 3x(2x-1)-1(2x-1)=(3x-1)(2x-1)(x-1)=0$.,
therefore, the solution to the equation is,
$3x-1=0$, or $2x-1=0$ or $x=1$
$x=1/3$ $x=1/2$
$x=${$1/3,1/2,1$}
