From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
This one's trying to fool you, because the polynomial almost looks like a difference of two squares, but it isn't. How dare it try to pull the wool over our eyes? Doesn't it know it's an open weave anyway?
First, we pull out a common factor.
3(y2 – 9x2)
The part in parentheses is a difference of two squares, so it can be written as:
(y + 3x)(y – 3x)
To arrive at the final answer, we need to remember to replace the 3 we pulled out. Like you need to remember to replace the roll of toilet paper unless you want your mother screaming at you. Like so:
3(y + 3x)(y – 3x)
Factor the polynomial 8x2 – 56x + 98.
The terms have a common factor of 2, so the first thing we do is pull that out.
2(4x2 – 28x + 49)
Now we need to factor the part in parentheses if possible. Since the middle term has a negative sign, we hope we can factor this part like so:
▲2 – ■2
Since ▲2 = 4x2 and ■2 = 49, we need ▲ = 2x and ■ = 7.
Squaring (2x – 7) does give us 4x2 – 28x + 49, so we can factor the original polynomial as:
2(2x – 7)2
This result was so much more satisfying than that of the last example. Like the last bite of a slice of banana cream pie. Actually, more like the first bite, because then there are still all those other bites left.