(4x^2-7x-11) Divided By (x+1)

Jasonbradley

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Jun 16, 2024

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Dividing Polynomials: (4x^2 - 7x - 11) ÷ (x + 1)

This article will demonstrate how to divide the polynomial (4x^2 - 7x - 11) by (x + 1) using polynomial long division.

Understanding Polynomial Long Division

Polynomial long division is a method used to divide polynomials, similar to how long division is used to divide numbers. The process involves:

1. Setting up the division: Write the dividend (4x^2 - 7x - 11) inside the division symbol and the divisor (x + 1) outside.
2. Dividing the leading terms: Divide the leading term of the dividend (4x^2) by the leading term of the divisor (x). This gives you 4x.
3. Multiplying the quotient: Multiply the quotient (4x) by the entire divisor (x + 1) to get 4x^2 + 4x.
4. Subtracting: Subtract the result from the dividend.
5. Bringing down the next term: Bring down the next term of the dividend (-11).
6. Repeat: Repeat steps 2-5 with the new polynomial until the degree of the remainder is less than the degree of the divisor.

Steps for Dividing (4x^2 - 7x - 11) by (x + 1)

1. Set up the division:

        _______
x + 1 | 4x^2 - 7x - 11 

2. Divide the leading terms: 4x^2 / x = 4x

        4x     
x + 1 | 4x^2 - 7x - 11 

3. Multiply the quotient: 4x * (x + 1) = 4x^2 + 4x

        4x     
x + 1 | 4x^2 - 7x - 11 
        -(4x^2 + 4x)

4. Subtract:

        4x     
x + 1 | 4x^2 - 7x - 11 
        -(4x^2 + 4x)
              -11x - 11

5. Bring down the next term:

        4x     
x + 1 | 4x^2 - 7x - 11 
        -(4x^2 + 4x)
              -11x - 11

6. Repeat: -11x / x = -11

        4x - 11   
x + 1 | 4x^2 - 7x - 11 
        -(4x^2 + 4x)
              -11x - 11
              -(-11x - 11)

7. Subtract:

        4x - 11   
x + 1 | 4x^2 - 7x - 11 
        -(4x^2 + 4x)
              -11x - 11
              -(-11x - 11)
                    0

The Result

The result of the division is: (4x^2 - 7x - 11) ÷ (x + 1) = 4x - 11

The remainder is 0, indicating that (x + 1) is a factor of (4x^2 - 7x - 11).