Question
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?
Solution
4
(104 Votos)
Renata Maria
Profissional · Tutor por 6 anos
Resposta
To find the mistake in Cam's synthetic division, let's go through the process step-by-step.The given polynomial is
, and we are dividing it by
.Step 1: Write down the coefficients of the polynomial in descending order of their powers. Since there is no
term, its coefficient is 0. So, the coefficients are 1, 0, 3, -4, and -2.Step 2: Write down the zero of the divisor
, which is 2.Step 3: Perform synthetic division using the zero and the coefficients.``` 2 | 1 0 3 -4 -2 | 2 4 14 -20 38 ------------------- 1 2 7 10 -26```Step 4: Interpret the result. The numbers in the bottom row represent the coefficients of the quotient and the remainder. So, the quotient is
and the remainder is -26.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.Therefore, the best description of Cam's mistake is that he made an error in the multiplication step of the synthetic division process.