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 1 -1 square -1 10 -3 12 120 square 13 -40square 2 Item 1 Item 2 Item Item 4 Item 5 Item 6 Item 7

To find $p(-3)$ using synthetic substitution, we will use 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: Set up the synthetic array with the value $x = -3$:<br />$\begin{array}{r|rrrrr}<br />-3 & 1 & -1 & 1 & -1 & 10 \\<br />\end{array}$<br /><br />Step 3: Perform synthetic substitution:<br />$\begin{array}{r|rrrrr}<br />-3 & 1 & -1 & 1 & -1 & 10 \\<br /> & & -3 & 12 & 120 & -360 \\<br />\hline<br /> & 1 & -4 & 13 & -40 & -350 \\<br />\end{array}$<br /><br />The final row of the synthetic array gives us the coefficients of the resulting polynomial when $x = -3$. Therefore, $p(-3) = -350$.<br /><br />Answer: $p(-3) = -350$