- #1

karush

Gold Member

MHB

- 3,269

- 5

$\text{factor}$

$g(x)=2x^3+5x^2-28x-15$

$\text{synthetic division}$

$\begin{array}{c|rr}

& 2 & 5 &-28 &-15 \\

&&6&33 & 15\\ \hline

3&2&11&5&0

\end{array}$

$\text{thus }\\$

$2x^2+11x+5$

$\text{use quadradic formula}$

$\begin{align*}

x=\frac{-(11)\pm\sqrt{(11)^2-4(2)(5)}}{2(1)}

&=\frac{-11\pm\sqrt{81}}{2}

=\frac{-11\pm9}{2}

\end{align*}$

$x=-10,-1 \quad g(x)=(x+10)(x+1)(x-3)$

hopefully

comment?

$g(x)=2x^3+5x^2-28x-15$

$\text{synthetic division}$

$\begin{array}{c|rr}

& 2 & 5 &-28 &-15 \\

&&6&33 & 15\\ \hline

3&2&11&5&0

\end{array}$

$\text{thus }\\$

$2x^2+11x+5$

$\text{use quadradic formula}$

$\begin{align*}

x=\frac{-(11)\pm\sqrt{(11)^2-4(2)(5)}}{2(1)}

&=\frac{-11\pm\sqrt{81}}{2}

=\frac{-11\pm9}{2}

\end{align*}$

$x=-10,-1 \quad g(x)=(x+10)(x+1)(x-3)$

hopefully

comment?

Last edited: