Q: Solve for x:
22x + 2x+2 – 12 = 0
A: The first thing we need to notice (from practice and experience) is that we can re-write this like so using our knowledge / rules of exponents:
(2x)2 + 22*2x – 12 = 0
Now simplify a little:
(2x)2 + 4*2x – 12 = 0
So, look at this in a new light. What if we substitute each 2x with y?
(2x)2 + 4*2x – 12 = 0 turns into y2 + 4*y – 12 = 0
(this isn’t necessary, but is helpful for visualization)
We see this is in the form of a quadratic and can be factored:
(y + 6)(y – 2) = 0
So, y = -6 or y = 2
Remember, y was a substitution for 2x. So, we really have:
2x = -6 or 2x = 2
Solve each equation separately. Let’s start with:
Continue reading Solving Exponential Equations by Factoring
Q: Solve for n:
4n2 + 3 = 7n
Answer: Since there is an n-squared term, this is a quadratic equation. In order to solve this, we need to set the whole equation equal to 0 first (so, let’s subtract the 7n over to the left side of the equation):
4n2 – 7n + 3 = 0 [notice that I put the n’s in order of n-squared, n, and then the constant 3]
Now, there are a few methods you may have learned to can help you solve this: 1) Factoring or 2) Quadratic Formula or 3) Completing the Square.
Continue reading Solving a quadratic
Q: Factor by Grouping: -4q3u-2q2u-4qu
Continue reading Factor by grouping
Q: Factor completely: 9m³n – 19m²n² + 2mn³
Continue reading Factoring with 2 letters!
Factoring is an art. There is no right or wrong way to think about factoring, there is no formula to apply, there is no single method that works… Many methods work. Many lines of thinking work. Factoring is hard. But, I will help you through it.
There are many ways to factor, many things to factor, many uses of factoring, many, many, many… I am going to start us at square 1.
Continue reading Factoring 101
Q: Segment NY has a midpoint, R. NR = x² – x – 2 and RY = 5x – 7. Find x and the length of NY.
Continue reading Midpoint Questions w/ factoring
Q: Geometry and Angles
Ray RY bisects angle NRT
Measure of angle NRY = 2x² + 6x
Measure of angle YRT = 10x + 6
Find x and the measure of angle YRT
Continue reading Geometry (w/ factoring)
View the Factoring 101 post to get started with the basics of factoring first!
Q: Solve by factoring: x² – 7x = 78
Continue reading Solve by factoring example