Question

Use the long division method to find the result when 4x³+7x²-8x-14 is divided by 4x+7. If there is a remainder, express the result in the form q(x)+r(x)/b(x).

Answer 1

a

Explanation:

Answer 2

First, we write the polynomial in descending order of degree:

4x³+7x²-8x-14

Now, we start dividing the first term of the dividend by the divisor:

x²

___________

4x+7|4x³+7x²-8x-14

We multiply x² by 4x+7 to get:

x²

___________

4x+7|4x³+7x²-8x-14

4x³+7x²

-8x

Now we bring down the next term:

x²-2

___________

4x+7|4x³+7x²-8x-14

4x³+7x²

-8x-14

+8x+14

_______

0

The remainder is zero, which means that 4x+7 is a factor of 4x³+7x²-8x-14. The quotient is x²-2.

Therefore, the result when 4x³+7x²-8x-14 is divided by 4x+7 is:

4x³+7x²-8x-14 = (4x+7)(x²-2) + 0

So, the quotient is x²-2, and there is no remainder.