# Algebra 1 : How to factor a polynomial

## Example Questions

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### Example Question #1 : How To Factor A Polynomial

Factor the following:

Explanation:

We will discuss coefficients in the general equation:

In this case,  is positive and  is negative, and , so we know our answer involves two negative numbers that are factors of  and add to . The answer is:

### Example Question #1 : Solving By Factoring

Solve for

Explanation:

This is a factoring problem so we need to get all of the variables on one side and set the equation equal to zero. To do this we subtract  from both sides to get

Think of the equation in this format to help with the following explanation.

We must then factor to find the solutions for . To do this we must make a factor tree of  which is 28 in this case to find the possible solutions. The possible numbers are , , .

Since  is positive we know that our factoring will produce two positive numbers.

We then use addition with the factoring tree to find the numbers that add together to equal . So ,  , and

Success! 14 plus 2 equals . We then plug our numbers into the factored form of

We know that anything multiplied by 0 is equal to 0 so we plug in the numbers for  which make each equation equal to 0 so in this case .

### Example Question #1 : Factoring Polynomials

Solve by factoring:

Explanation:

By factoring one gets

Now setting each of the two factors to 0 (using the zero property), one gets

or

### Example Question #3 : Factoring Polynomials

Solve by using the quadratic formula:

Explanation:

we get

resulting in

and

### Example Question #4 : Factoring Polynomials

Find the axis of symmetry and the minimum/maximum value of the following quadratic equation in standard form:

, Minimum value of the function

, Minimum value of the function

, Minimum value of the function

, Maximum value of the function

, Maximum value of the function

, Maximum value of the function

Explanation:

If we convert the given quadratic  equation from standard form to vertex form, we get:

Hence the axis of symmetry is

and the minimum value at  is  ( this function is concave down)

### Example Question #1 : How To Factor A Polynomial

Write the equation of a circle having (3, 4) as center and a radius of .

Explanation:

The center is located at (3,4) which means the standard equation of a circle which is:

becomes

which equals to

### Example Question #5 : Factoring Polynomials

Factor:

Explanation:

This is a difference of cubes.

are all cubes. So the formula for factoring this expression is:

### Example Question #6 : Factoring Polynomials

Equation of a circle in standard form:

with center  and radius equal to .

Find out the radius and center of circle from the given equation in expanded form:

Center :  and the radius =

The center is  and the radius =

The center is  and the radius =

Explanation:

The given equation in standard form :

Hence the center:  and the radius = .

### Example Question #7 : Factoring Polynomials

Factor:

Explanation:

Difference of 2 squares is equal to the product of the sum and difference of two terms.

The two terms here are  and  and the product therefore equals to

### Example Question #8 : Factoring Polynomials

Simplify:

Explanation:

By factoring both the numerator and the denominator we get the following:

If we simplify we get:

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