**“After performing polynomial long division, the answer may be checked by multiplying ____ by the ____ and then adding the ____. You should obtain the ____.”**

This **article aims to fill the blanks in the sentence**. The article uses the concept of **long division by the polynomial**. A**Â long division polynomial** is an **algorithm**Â for dividing a polynomial by **another polynomial**Â of the same or**Â lower degree**. **Long division of polynomials**Â also consists of a **divisor**, **quotient**, **division**, and **remainder**Â as in the long division method of numbers.

In algebra, the **division of algebraic expressions**Â can be done in these ways:

–**Dividing**Â a monomial by **another**Â **monomial.**

–**Dividing**Â a polynomial by **a monomial.**

–**Dividing**Â a polynomial by**Â a binomial.**

–**Dividing**Â a polynomial by **another polynomial.**

**Steps for long division of polynomial**

Here are the**Â steps**Â for the**Â long division of polynomials:**

**Step 1.**Â Arrange the members in **descending order of their indices**Â (if required). Write **missing terms with zero**Â as their**Â coefficient.**

**Step 2.**Â For the** first term of the quotient**, divide the **dividend**‘s first term by the **divisor’s first term.**

**Step 3.**Â **Multiply** this term of theÂ **quotient by the divisor**Â to get the product.

**Step 4.**Â **Subtract this product from the dividend**Â and reduce the following term (if any). The difference and the reduced term will form a **new dividend**.

**Step 5.**Â Do this until you get a remainder, which can be **zero or a lower index than the divisor**.

**Expert Answer**

After a **long division by a polynomial**, the answer can be checked by multiplying the **quotient**Â by the**Â divisor**Â and then adding the **remainder**. You should get a **dividend.**

In algebra, **long division** by a polynomial is an algorithm for dividing a polynomial by another polynomial of theÂ **same or lower degree**, a **generalized version**Â of a well-known arithmetic technique called **long division.**Â This can easily be done manually as it breaks an otherwise complex division problem into smaller ones. Sometimes using a **shortened version called synthetic division**Â is faster, with **less typing and less computation**.

**Numerical Result**

AfterÂ **long division**Â by a **polynomial**, the answer can be checked by **multiplying**Â theÂ **quotient**Â by the **divisor**Â and then adding the **remainder**. You should get a **dividend**.

**Example**

**Verify that the given statement is true or false:**

**“After a long division by a polynomial, the answer can be checked by dividing the quotient by divisor and then adding the remainder. You should get a dividend.”**

**Solution**

The**Â given statement is False**. The **correct statement** is given as:

After a **long division**Â by a **polynomial**, the answer can be checked by **multiplying** theÂ **quotient**Â by the **divisor**Â and then adding the **remainder**. It would help if you got a **dividend**.