1 3 -4 -2 2 10 12 1 5 6 10 Cam divided (x^4+3x^2-4x-2) by factor of (x-2) using synthetic division. His work is shown above . Which best describes his mistake?

To find the mistake in Cam's synthetic division, let's go through the process step-by-step.<br /><br />The given polynomial is \(x^4 + 3x^2 - 4x - 2\), and we are dividing it by \(x - 2\).<br /><br />Step 1: Write down the coefficients of the polynomial in descending order of their powers. Since there is no \(x^3\) term, its coefficient is 0. So, the coefficients are 1, 0, 3, -4, and -2.<br /><br />Step 2: Write down the zero of the divisor \(x - 2\), which is 2.<br /><br />Step 3: Perform synthetic division using the zero and the coefficients.<br /><br />```<br /> 2 | 1 0 3 -4 -2<br /> | 2 4 14 -20 38<br /> -------------------<br /> 1 2 7 10 -26<br />```<br /><br />Step 4: Interpret the result. The numbers in the bottom row represent the coefficients of the quotient and the remainder. So, the quotient is \(x^3 + 2x^2 + 7x + 10\) and the remainder is -26.<br /><br />Comparing this with Cam's work, we can see that Cam's mistake was in the second row. He wrote 10 instead of 14, and -2 instead of -20. This indicates that he made a mistake in the multiplication step.<br /><br />Therefore, the best description of Cam's mistake is that he made an error in the multiplication step of the synthetic division process.