Question

Simplify:

4x^3 – 31x^2 – 39x – 54 by X-9

Answer 1

To simplify the expression 4x^3 - 31x^2 - 39x - 54 by (x - 9), use polynomial long division.

Step-by-step explanation:

To simplify the expression 4x^3 - 31x^2 - 39x - 54 by (x - 9), we can use polynomial long division.

1. Divide the first term of the polynomial (in this case, 4x^3) by the first term of the binomial (x). This gives us 4x^2.
2. Multiply the divisor (x - 9) by the quotient (4x^2). This gives us 4x^3 - 36x^2.
3. Subtract the result from the original polynomial. This gives us -31x^2 + 36x^2 - 39x - 54.
4. Repeat the process with -31x^2 + 36x^2 - 39x - 54.
5. Continue dividing and subtracting until there are no more terms to divide.

The final result after simplifying is 4x^2 - 36x - 115.