GED Math : Single-Variable Algebra

Example Questions

Example Question #11 : Algebra

Express 286 in base five.

Explanation:

To convert a base ten number to base five, divide the number by five, with the remainder being the digit in the units place; continue, dividing each successive quotient by five and putting the remainder in the next position to the left until the final quotient is less than five.

- 1 is the last digit.

- 2 is the second-to-last digit.

- 1 is the third-to-last digit; 2 is the first digit.

286 is equal to .

Example Question #12 : Algebra

Simplify the following:

Explanation:

Group all like terms by their order:

Simplify:

Example Question #13 : Algebra

Simplify the following:

Explanation:

This can be solved using the FOIL method.  The steps are shown below.

Therefore, after reordering, the answer is:

Simplify:

Explanation:

Example Question #15 : Algebra

Factor completely:

Explanation:

Use the grouping technique, then distribute out the greatest common factor of each group as follows:

Example Question #11 : Algebra

Factor completely:

Explanation:

The common factor of the terms  and  can be found as follows:

, and the lesser of the two powers of  is ; therefore, , their product. Distribute this out:

This is as far as we can go with the factoring.

Example Question #11 : Simplifying, Distributing, And Factoring

Factor completely:

Explanation:

Use the grouping technique - group the terms into pairs, then factor out the greatest common factor of each pair.

Example Question #11 : Simplifying, Distributing, And Factoring

Factor completely:

Explanation:

A polynomial of the form  can be factored by first splitting the term into two terms whose coefficients add up to  and have product , then factoring out by the grouping technique.

We are looking for two integers whose sum is  and whose product is . Through some trial and error, we can see that the integers are , so:

Example Question #12 : Algebra

Factor completely:

Explanation:

First, factor out the greatest common factor of the terms, which is :

is the difference of squares, so we can factor further:

Simplify: