DIRECTIONS: Use the information to answer Parts A and B. p(x)=x^4-x^3+x^2-x+10 Part A Use synthetic substitution to find p(-3) Enter the correct values or expressions in the boxes to complete the synthetic array. Show Hints

To find $p(-3)$ using synthetic substitution, we will set up a synthetic array with the coefficients of the polynomial $p(x)$ and the value $-3$.<br /><br />Step 1: Write down the coefficients of $p(x)$ in descending order of their powers:<br />$1, -1, 1, -1, 10$<br /><br />Step 2: Bring down the first coefficient (1) as it is.<br /><br />Step 3: Multiply the value $-3$ by the number just brought down (1) and write the result under the next coefficient (-1).<br /><br />Step 4: Add the numbers in the second column to get the new number to bring down.<br /><br />Step 5: Repeat steps 3 and 4 until all coefficients have been used.<br /><br />The synthetic array should look like this:<br /><br />$\begin{array}{r|rrrrr}<br />-3 & 1 & -1 & 1 & -1 & 10 \\<br /> & & -3 & 12 & -33 & 102 \\<br />\hline<br /> & 1 & -4 & 13 & -34 & 112 \\<br />\end{array}$<br /><br />The last row of numbers represents the coefficients of the resulting polynomial after synthetic substitution. The last number (112) is the value of $p(-3)$.<br /><br />Therefore, $p(-3) = 112$.