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Use synthetic division to find the quotient and the remainder.

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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

 

asked Sep 3, 2014 in ALGEBRA 2 by tonymate Pupil

1 Answer

+1 vote
 
Best answer

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.

image

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

image

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

5+(-8) = - 3

image

 

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

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

image

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

Write the product under the next coefficient, - 4 and add : -4+(4) = 0.

image

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.

answered Sep 3, 2014 by bradely Mentor
selected Sep 3, 2014 by tonymate

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