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. square Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Item 7

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 $x = -3$.<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 the first number in the synthetic array.<br /><br />Step 3: Multiply the number just brought down (1) by the value of $x$ (-3) and write the result below the next coefficient (-1).<br /><br />Step 4: Add the numbers in the second column to get the next number in the synthetic array.<br /><br />Step 5: Repeat steps 3 and 4 for each column.<br /><br />The synthetic array should look like this:<br /><br />$\begin{array}{r|rrrrr}<br />-3 & 1 & -1 & 1 & -1 & 10 \\<br /> & & -3 & 12 & -11 & 30 \\<br />\hline<br /> & 1 & -4 & 13 & -12 & 40 \\<br />\end{array}$<br /><br />Therefore, the completed synthetic array is:<br /><br />$\begin{array}{r|rrrrr}<br />-3 & 1 & -1 & 1 & -1 & 10 \\<br /> & & -3 & 12 & -11 & 30 \\<br />\hline<br /> & 1 & -4 & 13 & -12 & 40 \\<br />\end{array}$<br /><br />So, the correct values or expressions to complete the synthetic array are:<br />Item 1: -3<br />Item 2: 1<br />Item 3: -1<br />Item 4: 1<br />Item 5: -1<br />Item 6: 10<br />Item 7: 40