Chapter 8.5, Problem 7WE

To determine

To find $P\left(c\right)$ for the given polynomial $P\left(x\right)$ and the given number c using synthetic substitution.

Answer to Problem 7WE

The value of $P\left(c\right)$ when $P(x)=2x^4-x^3+x;c=-\frac{3}{2}$ is $P(-\frac{3}{2})=10$

Explanation of Solution

Given information:

The polynomial is $P(x)=2x^4-x^3+x;c=-\frac{3}{2}$

Calculation :

Using synthetic substitution, the value of $P\left(c\right)$ is obtained as:

  $c\to -\overline{)\frac{3}{2}}$ 2 $-$ 1 0 1 $-$ 2

  $-$36$-$9 12

4 6 $-$ 8 | $10\leftarrow P(c)$

Therefore, $P\left(-\frac{3}{2}\right)=10$