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Morgan begins to use synthetic division to divide x^4+x^3-6x^2-4x+8 by x-2, as shown below. Which of the following shows the correct values to replace the question marks,and also gives the quotient?

Morgan begins to use synthetic division to divide x^4+x^3-6x^2-4x+8 by x-2, as shown-example-1
User Sovos
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1 Answer

4 votes

Answer:

B. 2, 6, 0, 8; x^3 + 3x^2 - 4

Step-by-step explanation:

When we divide x^4+x^3-6x^2-4x+8 by x-2, the synthetic division is equal to

Because the first 1 is moved down. Then, 1 x 2 = 2, so we type 2 under the next number and add, so 1 + 2 = 3

We continue with the same proccess, so 3 x 2 = 6 and -6 + 6 = 0

0 x 2 = 0 and -4 + 0 = -4

-4 x 2 = -8 and 8 - 8 = 0

Therefore, the missing numbers are 2, 6, 0 and -8 and the quotient is equal to

x^3 + 3x^2 + 0x - 4

x^3 + 3x^2 - 4

Because each number below the line is the coefficient of the powers of x in descendent order.

So, the answer is

B. 2, 6, 0, 8; x^3 + 3x^2 - 4

Morgan begins to use synthetic division to divide x^4+x^3-6x^2-4x+8 by x-2, as shown-example-1
User Askewchan
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