Algebra II : Polynomials

Example Questions

Example Question #21 : Simplifying Polynomials

Simplify the following expressions by combining like terms:

Explanation:

Distribute the negative sign through all terms in the parentheses:

Add the second half of the expression, to get:

Example Question #21 : Simplifying Polynomials

Write as a polynomial in standard form:

Explanation:

Replace: :

Example Question #6 : How To Add Polynomials

Combine:

Explanation:

When combining polynomials, only combine like terms. With the like terms, combine the coefficients. Your answer is

Example Question #22 : Simplifying Polynomials

Simplify this expression:

Not able to simplify further

Explanation:

Don't be scared by complex terms! First, we follow our order of operations and multiply the  into the first binomial. Then, we check to see if the variables are alike. If they match perfectly, we can add and subtract their coefficients just like we could if the expression was .

Remember, a variable is always a variable, no matter how complex! In this problem, the terms match after we follow our order of operations! So we just add the coefficients of the matching terms and we get our answer:

Example Question #119 : Polynomials

Simplify the following expression.

Explanation:

First, we will need to distribute the minus sign.

Then, combine like terms.

Example Question #81 : Variables

Divide:

Explanation:

First, rewrite this problem so that the missing  term is replaced by

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat this process with each difference:

, the second term of the quotient

One more time:

, the third term of the quotient

, the remainder

The quotient is  and the remainder is ; this can be rewritten as a quotient of

Example Question #21 : Simplifying Polynomials

Divide:

Explanation:

Divide the leading coefficients to get the first term of the quotient:

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat these steps with the differences until the difference is an integer. As it turns out, we need to repeat only once:

, the second term of the quotient

, the remainder

Putting it all together, the quotient can be written as .

Explanation:

Example Question #11 : Monomials

Explanation:

Use the distributive property to obtain each term:

Example Question #23 : Simplifying Polynomials

Simplify the polynomials.  Assume that no variables equal zero.