GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #411 : Algebra

Factor the expression completely:

Possible Answers:

Correct answer:

Explanation:

This expression can be rewritten:

As the difference of squares, this can be factored as follows: 

As the sum of squares with relatively prime terms, the first factor is a prime polynomial. The second factor can be rewritten as the difference of two squares and factored:

Similarly, the middle polynomial is prime; the third factor can be rewritten as the difference of two squares and factored:

This is as far was we can factor, so this is the complete factorization.

Example Question #2 : Understanding Factoring

Where does this function cross the -axis?

Possible Answers:

It never crosses the x axis.

Correct answer:

Explanation:

Factor the equation and set it equal to zero.  . So the funtion will cross the -axis when

Example Question #412 : Algebra

If , and , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

This questions tests the formula: .

Therefore, we have . So

Example Question #413 : Algebra

Factor:

Possible Answers:

Correct answer:

Explanation:

 can be grouped as follows:

 is a perfect square trinomial, since 

 

Now use the difference of squares pattern:

Example Question #414 : Algebra

Factor completely:

Possible Answers:

Correct answer:

Explanation:

Group the first three terms and the last three terms, then factor out a GCF from each grouping:

We try to factor  as a sum of cubes; however, 5 is not a perfect cube, so the binomial is a prime.

To factor out , we try to factor it into , replacing the question marks with two integers whose product is 2 and whose sum is 3. These integers are 1 and 2, so 

The original polynomial has  as its factorization.

Example Question #1 : Solving By Factoring

Factor completely: 

Possible Answers:

Correct answer:

Explanation:

Group the first three terms and the last three terms, then factor out a GCF from each grouping:

 is the sum of cubes and can be factored using this pattern: 

We try to factor out the quadratic trinomial as , replacing the question marks with integers whose product is 1 and whose sum is . These integers do not exist, so the trinomial is prime.

The factorization is therefore

Example Question #411 : Algebra

Factor:

Possible Answers:

Correct answer:

Explanation:

 can be grouped as follows:

The first three terms form a perfect square trinomial, since 

, so

Now use the dfference of squares pattern:

Example Question #415 : Algebra

Solve for  when .

Possible Answers:

Correct answer:

Explanation:

Example Question #416 : Algebra

Solve for  when .

Possible Answers:

and

and

and

and

Correct answer:

and

Explanation:

and

and

 

Example Question #417 : Algebra

Solve for :

 

Possible Answers:

and

 

and

and

and

Correct answer:

and

Explanation:

and

and

 

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