### All Algebra 1 Resources

## Example Questions

### Example Question #4591 : Algebra 1

Find the GCF (greatest common factor) of the following polynomial expression.

**Possible Answers:**

**Correct answer:**

Let's find the GCF of the coefficients, first. Our coefficients are 3, 9, and -15. The GCF is 3. 3 is the biggest number that can divide EACH of the numbers without leaving a remainder.

So, 3 is the first part of our GCF.

Next, look at the variables. THERE IS NO COMMON VARIABLE! The first term has an "r" variable, but the second term only has a "q" variable. They do not have anything in common, so we cannon factor out any variables.

So, the only factor all of the terms have in common is "3," and when you divide each of the terms by 3, we get:

### Example Question #45 : How To Factor A Polynomial

Factor the following polynomial expression completely. Use the "factor-by-grouping" method.

(Method is demonstrated in the answer explanation)

**Possible Answers:**

**Correct answer:**

At first, it looks like none of the the terms have any factors in common. But here's how we factor by "grouping": we separate the four terms into two groups, with two terms in each group. Then, we find the GCF of each separate group.

First group: 6a + 3

Second group: 8ab + 4b

Start with the first group. The GCF is "3," since that's the biggest number that can divide each term without leaving a remainder. So, group 1 is:

Second group. The GCF is 4b. Check it, if you're not sure. That means that when group 2 is factored, we get:

So, since both group 1 and group 2 were being ADDED to each other in our original expression, we can simply add the two factored groups to each other:

The expression is still the same, we've just rewritten it in factored form. If you multiply through the parentheses, you'll see that we still have the same original expression:

But now, notice that the two factored terms have something in common! They each have the factor

So, we can divide (2a+1) from both terms, leaving us with:

### Example Question #46 : How To Factor A Polynomial

Factor the following polynomial expression completely, using the "factor-by-grouping" method.

**Possible Answers:**

**Correct answer:**

Group the first two terms together:

Find the GCF:

Group the second two terms together:

Find the GCF:

The two factored terms both have as their GCF.

So, factoring out from each term gives us:

### Example Question #71 : Intermediate Single Variable Algebra

Which of the following expressions is a factor of this polynomial: 3x² + 7x – 6?

**Possible Answers:**

(3x + 2)

(x + 3)

(x – 3)

(x – 3x)

(3x – 6)

**Correct answer:**

(x + 3)

The polynomial factors into (x + 3) (3x - 2).

3x² + 7x – 6 = (a + b)(c + d)

There must be a 3x term to get a 3x² term.

3x² + 7x – 6 = (3x + b)(x + d)

The other two numbers must multiply to –6 and add to +7 when one is multiplied by 3.

b * d = –6 and 3d + b = 7

b = –2 and d = 3

3x² + 7x – 6 = (3x – 2)(x + 3)

(x + 3) is the correct answer.

### Example Question #72 : Intermediate Single Variable Algebra

Factor the polynomial .

**Possible Answers:**

y = (x – 3)(x + 2)

y = (x + 6)(x + 1)

y = (x – 2)(x + 3)

y = (x + 3)(x + 2)

y = (x + 5)(x + 1)

**Correct answer:**

y = (x + 3)(x + 2)

The product of the last two numbers should be 6, while the sum of the products of the inner and outer numbers should be 5x. Factors of six include 1 and 6, and 2 and 3. In this case, our sum is five so the correct choices are 2 and 3. Then, our factored expression is (x + 2)(x + 3). You can check your answer by using FOIL.

y = x^{2} + 5x + 6

2 * 3 = 6 and 2 + 3 = 5

(x + 2)(x + 3) = x^{2} + 5x + 6

### Example Question #81 : Polynomials

Factor:

**Possible Answers:**

The expression cannot be factored.

**Correct answer:**

Because both terms are perfect squares, this is a difference of squares:

The difference of squares formula is .

Here, a = x and b = 5. Therefore the answer is .

You can double check the answer using the FOIL method:

### Example Question #361 : Polynomials

Factor:

**Possible Answers:**

**Correct answer:**

The solutions indicate that the answer is:

and we need to insert the correct addition or subtraction signs. Because the last term in the problem is positive (+4), both signs have to be plus signs or both signs have to be minus signs. Because the second term (-5x) is negative, we can conclude that both have to be minus signs leaving us with:

### Example Question #92 : Polynomials

Factor the following:

**Possible Answers:**

**Correct answer:**

Using the FOIL rule, only yields the same polynomial as given in the question.

### Example Question #93 : Polynomials

Factor the following polynomial:

**Possible Answers:**

Can't be factored

**Correct answer:**

When asked to factor a difference of squares, the solution will always be the square roots of the coefficients with opposite signs in each pair of parentheses.

### Example Question #52 : How To Factor A Polynomial

Solve by factoring:

**Possible Answers:**

Prime

**Correct answer:**

Here . Multiply and and you get which can be factored as and and when one adds and you get . Hence the quadratic equation can be rewritten as

Now you factor by grouping the first two terms and the last two terms giving us

which can be further factored resulting in

By setting each of the two factors to 0 we get

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