Division of Polynomial

To find the remainder when the polynomial (8y + 8y^2 + 7) is divided by (1 - y), we can use the method of polynomial division.

Polynomial Division

Polynomial division is a method used to divide one polynomial by another polynomial. It is similar to long division, but instead of dividing numbers, we divide polynomials.

Step 1: Set up the Division

To begin, we set up the division by writing the dividend (the polynomial being divided) and the divisor (the polynomial we are dividing by) in the appropriate places.

Dividend: 8y + 8y^2 + 7
Divisor: 1 - y

Step 2: Divide the Leading Term

Next, we divide the leading term of the dividend by the leading term of the divisor.

Leading term of the dividend: 8y^2
Leading term of the divisor: 1

The quotient is 8y, which is written above the line.

Step 3: Multiply the Divisor by the Quotient

Now, we multiply the divisor by the quotient and write the result below the dividend.

Quotient: 8y
Divisor: 1 - y

8y + 8y^2 + 7
- (8y - 8y^2)
_______________
16y^2 + 7

Step 4: Subtract and Repeat

Next, we subtract the product from the dividend and bring down the next term.

8y + 8y^2 + 7
- (8y - 8y^2)
_______________
16y^2 + 7
- (16y^2 - 16y)
_______________
16y + 7

Step 5: Repeat the Process

We repeat the process of dividing, multiplying, subtracting, and bringing down until we have no more terms to bring down.

In this case, we have no more terms to bring down.

Step 6: Determine the Remainder

The remainder is the last term we obtained in the division process. In this case, the remainder is 16y + 7.

Therefore, the remainder when (8y + 8y^2 + 7) is divided by (1 - y) is 16y + 7.

May be 0