Polynomials

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Pre-Algebra › Polynomials

Questions 1 - 10
1

Solve for :

Explanation

Add 45 to both sides:

2

Solve:

Imaginary roots

Explanation

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract 56 from both sides of the equation.

Factorize the left side.

These can be split into 2 separate equations.

The solutions are:

3

Solve:

Imaginary roots

Explanation

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract 56 from both sides of the equation.

Factorize the left side.

These can be split into 2 separate equations.

The solutions are:

4

Solve for :

Explanation

Add 45 to both sides:

5

Simplify:

This expression is already simplified

Explanation

The product rule tells us that if we're multiplying 2 terms with exponents, we add the exponents. However, that is only applicable for 2 terms with the same base. In this case, our bases are different variables, so we can't use the product rule. This expression is as simplified as possible.

6

Evaluate the expression if .

Explanation

We can replace each instance of in the original expression with 3.

Now, solve using order of operations:

7

Simplify:

Explanation

8

Simplify:

Explanation

9

Simplify:

This expression is already simplified

Explanation

The product rule tells us that if we're multiplying 2 terms with exponents, we add the exponents. However, that is only applicable for 2 terms with the same base. In this case, our bases are different variables, so we can't use the product rule. This expression is as simplified as possible.

10

Evaluate the expression if .

Explanation

We can replace each instance of in the original expression with 3.

Now, solve using order of operations:

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