Precal Help????

Question

Use synthetic division to find the quotient and remainder.

14 − 27x − 27x2 + 54x3

x − (2/3)

quotient
remainder

Write the result of the division in the form 

p(x) = d(x) · q(x) + R(x),

 as in equation (2) in the text.

14 − 27x − 27x² + 54x³ = 

Answer 1

Use synthetic division to find .

The dividend is , and the root is 2/3.

Step 1 : Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown at the right.

Step 2 : Write the constant r of the divisor (x - r) to the left. In this case, . Bring the first coefficient, 54, down.

Step 3 : Multiply the first coefficient by r : . Write the product under the second coefficient, - 27. Then add the product and the second coefficient, - 27 : .

Step 4 : Multiply the sum, 9, by r : .

Write the product under the next coefficient, - 27 and add : .

Step 5 : Multiply the sum, , by r : .

Write the product under the next coefficient, 14 and add : . The remainder is 0.

The numbers along the bottom row are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend. Thus, the quotient is .

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