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Example Questions
Example Question #1 : How To Factor A Polynomial
Factor the following:
None of the available answers
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 :
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:
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:
For the quadeatic equation . Applying these to the quadratic formula
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
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 .
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:
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 =
Center : and the radius =
Center: and the radius =
The center is and the radius =
Center: and the radius =
The center is and the radius =
The given equation in standard form :
Hence the center: and the radius =
.
Example Question #7 : Factoring Polynomials
Factor:
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 #1 : How To Factor A Polynomial
Simplify:
By factoring both the numerator and the denominator we get the following:
If we simplify we get:
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