Answer
To divide ${{x}^{3}}+5{{x}^{2}}-7x+1$ by $x-4$ using synthetic division, the first step is to write $\left. {\underline {\,
4 \,}}\! \right| $ , $1$ , $5$ , $-7$ , $1$.
Work Step by Step
Let us consider,
$x-4\overline{\left){{{x}^{3}}+5{{x}^{2}}-7x+1}\right.}$.
And the coefficient of dividend is:
$\underbrace{1}_{\text{coe}\text{. of }{{x}^{3}}}\text{ }\underbrace{5}_{\text{coe}\text{. of }{{x}^{2}}}\text{ }\underbrace{-7}_{\text{coe}\text{. of }{{x}^{1}}}\text{ }\underbrace{1}_{\text{coe}\text{. of }{{x}^{0}}}$.
And the constant for the divisor is:
$x-\text{c}=x-4\Rightarrow \text{c}=4$.
We know that according to the synthetic division procedure, the first step is
$\left. {\underline {\,
4 \,}}\! \right| \text{ }1\text{ }5\text{ }-7\text{ }1$.
Thus, the first step is to write $\left. {\underline {\,
4 \,}}\! \right| $ $1$ $5$ $-7$ $1$.
