The Quotient Of (X4 + 5X3 – 3X – 15) And A Polynomial Is (X3 – 3). What Is The Polynomial?

Solving equations is one of the most important operations in mathematics and holds the key to unlocking many mysteries. One of these equations involves finding the polynomial when you know the quotient. This can be a challenging problem, but don’t worry – we are here to help. In this blog post, we will explore how to find a polynomial when you know its quotient with an example equation – (X4 + 5X3 – 3X – 15) divided by (X3 – 3). We will dig into the process of solving for the polynomial so that you understand how to apply this concept to other problems as well.

The Quotient of (x4 + 5×3 – 3x – 15) and a Polynomial is (x3 – 3)

When finding the quotient of two polynomials, the first step is to determine the degree of the polynomials. The degree of a polynomial is the highest exponent of the variable in the equation. In this example, the degree of the first polynomial is 4 and the degree of the second polynomial is 3.

To find the quotient, divide the coefficients of each term in the first polynomial by the coefficients of each term in the second polynomial. In this example, you would divide 4 by 1, 5 by -3, and -3 by -15. This gives you a quotient of x3 – 3.

What is the Polynomial?

A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable raised to a non-negative integer power and multiplied by a coefficient. An example of a polynomial is 3×2 – 5x + 2. The first term, 3×2, is called the “quadratic” term because its degree (the highest power to which the variable is raised) is 2. The second term, -5x, is called the “linear” term because its degree is 1. The last term, 2, is called the “constant” or “zeroth” term because it has no variables and therefore its degree is 0.

How to find the Polynomial

Assuming you are asking how to find the polynomial given the information in the title, you can use synthetic division to solve for the polynomial.

To use synthetic division, start by dividing the leading coefficient of the divisor into the leading coefficient of the dividend. In this case, that would be frac{1}{3} . Next, multiply frac{1}{3} by each term in the divisor and write them underneath the corresponding terms in the dividend (ignoring like terms). So far, you should have:

1 1 1
3 | X + X – X – = 3 | X – 3X + 3
– –
———
0

Next, add all of the numbers in each row except for the bottom row. The sum of each row will be a term in your answer. In this case:

1 1 1 4 1 1
3 | X + X – X – = 3 | X – 3X + 3 = (4)X – (9) + (3) = (4)X^2 – 6X + 3
– – — —
——— ———
0 0

Conclusion

In conclusion, we have determined that the polynomial required to reach the quotient with (X4 + 5X3 – 3X – 15) is (X3 – 3). This solution can be reached by inspecting both sides of the equation and solving for x. By understanding how polynomials work, it is possible to solve equations such as these quickly and efficiently. If you are struggling with another similar problem, hopefully this article has been a helpful resource in guiding your understanding of what needs to be done to find the right solution.