Use synthetic division to find the quotient and the remainder.

Question

P(x) = 4x³ + 5x² - 8x - 4 is divided by x + 2. Use synthetic division to find the quotient and the remainder. 

	A.	4x2 – 3x – 2; 0
	B.	4x2 + 3x + 2; 2
	C.	2x2 – 3x; –2
	D.	4x2 + 3x – 2; 0

 

Answer 1

he function is 4x³ + 5x² - 8x - 4, and the root is -2.

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 below.

Step 2 : Write the constant r of the divisor (x - r) to the left. In this case, -2. Bring the first coefficient, 4, down.

Step 3 : Multiply the first coefficient by r : (-2)(4) = -8. Write the product under the second coefficient, 5 and add :

5+(-8) = - 3

 

Step 4 : Multiply the sum, - 3, by r : (-2)(-3)=6.

Write the product under the next coefficient, -8 and add : -8+(6) = -2.

Step 5 : Multiply the sum, -2, by r : (-2)(-2) = 4.

Write the product under the next coefficient, - 4 and add : -4+(4) = 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 4x²-4x-2   and remainder is 0.

So option A is correct.