GED Math : Quadratic Equations

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #71 : Quadratic Equations

Multiply 

Possible Answers:

Correct answer:

Explanation:

Even though the expression uses letters in the place where it is common to find numbers, we should recognize it is still the multiplication of two binomials, and the FOIL process can be used here.

F: 

O: 

I: 

L: 

So we have 

Example Question #72 : Quadratic Equations

Expand the expression 

Possible Answers:

Correct answer:

Explanation:

You can use the FOIL method to expand the expression 

F:First 

O: Outer

I: Inner

L:Last

 

L-Last

F: 

O: 

I: 

L: 

 

 

Example Question #73 : Quadratic Equations

Simplify the following with FOIL

Possible Answers:

Correct answer:

Explanation:

Remember, FOIL stands for First-Outer-Inner-Last

Multiply the first terms 

Multiply the outer terms

Multiply the inner terms

Multiply the last terms

Now we simply add them all together

And combine like-terms

Example Question #74 : Quadratic Equations

Expand: 

Possible Answers:

None of the above

Correct answer:

Explanation:

We distribute each term in each parentheses to the terms of the other parentheses.

We get:

Which Simplifies:

We will arrange these from highest to lowest power, and adding a sign in between terms based on the coefficient of each term:

 

So, the answer is 

Example Question #75 : Quadratic Equations

Possible Answers:

Correct answer:

Explanation:

This is a quadratic equation, but it is not in standard form.

We express it in standard form as follows, using the FOIL technique:

Now factor the quadratic expression on the left. It can be factored as

where .

By trial and error we find that , so 

 

can be rewritten as

.

Set each linear binomial equal to 0 and solve separately:

The solution set is .

Example Question #76 : Quadratic Equations

Subtract:

Possible Answers:

Correct answer:

Explanation:

can be determined by subtracting the coefficients of like terms. We can do this vertically as follows:

 

By switching the symbols in the second expression we can transform this to an addition problem, and add coefficients:

Example Question #391 : Algebra

Add:

Possible Answers:

Correct answer:

Explanation:

can be determined by adding the coefficients of like terms. We can do this vertically as follows:

Example Question #392 : Algebra

Which of the following expressions is equivalent to the product?

Possible Answers:

Correct answer:

Explanation:

Use the difference of squares pattern

with  and  :

Example Question #393 : Algebra

Which of the following expressions is equivalent to the product?

Possible Answers:

Correct answer:

Explanation:

Use the difference of squares pattern

with  and  :

Example Question #394 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Start by factoring the numerator. Notice that each term in the numerator has an , so we can write the following:

Next, factor the terms in the parentheses. You will want two numbers that multiply to  and add to .

Next, factor the denominator. For the denominator, we will want two numbers that multiply to  and add to .

Now that both the denominator and numerator have been factored, rewrite the fraction in its factored form.

Cancel out any terms that appear in both the numerator and denominator.

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