Question

homework assignment 5.4 dividing polynomials score: 7/8 answered: 7/8 question 8 find the quotient and remainder using synthetic division: $\frac{x^{4}-2x^{3}-14x + 12}{x - 3}$ the quotient is the remainder is question help: video read written example message instructor

Explanation:

Step1: Set up synthetic division

Write the coefficients of the dividend \(x^{4}-2x^{3}+0x^{2}-14x + 12\) which are \(1,-2,0,-14,12\) and the zero of the divisor \(x - 3\) is \(3\).

Step2: Bring down the first coefficient

Bring down the first coefficient \(1\).

Step3: Multiply and add

Multiply \(3\times1 = 3\), add to the second - coefficient: \(-2+3=1\). Then multiply \(3\times1 = 3\), add to the third - coefficient: \(0 + 3=3\). Multiply \(3\times3 = 9\), add to the fourth - coefficient: \(-14 + 9=-5\). Multiply \(3\times(-5)=-15\), add to the fifth - coefficient: \(12+( - 15)=-3\).

Step4: Write the quotient and remainder

The numbers \(1,1,3,-5\) are the coefficients of the quotient polynomial \(x^{3}+x^{2}+3x - 5\) and the last number \(-3\) is the remainder.

Answer:

The quotient is \(x^{3}+x^{2}+3x - 5\)
The remainder is \(-3\)