Use synthetic division to solve (x4 – 1) ÷ (x – 1). what is the quotient?

Asked by maham237 @ 27/11/2020 in Mathematics viewed by 439 People

Answered by maham237 @ 27/11/2020

The correct answer is:

x³+x²+x+1.

Explanation:

First we write the polynomial out with all of the other powers of x, using 0 as their coefficients:

(1x⁴+0x³+0x²+0x-1)÷(x-1)

To perform synthetic division, we write the coefficients of the dividend in a row:

1 0 0 0 1

We take the 1 from x-1 and use it in the box. We then drop the first 1 from the row of coefficients down.

We multiply our 1 in the box by the 1 at the bottom; this is 1 and goes under the first 0 to the right of the 1 in the coefficients row. We now add this 0+1; this is 1 and goes at the bottom beside the other 1.

Multiply this by 1; this is 1 and goes under the second 0 from the left in the row of coefficients. Add this to the 0; this is 1 and goes at the bottom, to the right of the other two 1's.

Multiply this by 1; this is 1 and goes under the third and last 0 in the row of coefficients. Add this to the 0; this is 1 and goes at the bottom, to the right of the other three 1's.

Multiply this by 1; this is 1 and goes under the -1 in the row of coefficients. Add this to the -1; this is 0 and goes at the bottom, to the right of the four 1's. This 0 means there is no remainder and the quotient was evenly divided. It gives us

1 1 1 1 0

This means we have 1x³+1x²+1x+1 with no remainder.

Use synthetic division to solve (x4 – 1) ÷ (x – 1). what is the quotient?

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