Factoring helps you find the zeroes on a graph. After you factor a function you have a bunch of (x+a)(x-b)... all multiplied together and equal to your function f(x). So f(x)=(x+a)(x-b)... Then we set the factored form to zero..... why? Well sort of because we can solve it easily using the zero product property. So when we set the factored form to zero (x+a)=0 (x-b)=0 . . . What are we doing? Well we are finding the x-values that make 0=(x+a)(x-b)... Which is the same as finding when f(x)=0. f(x)=0 is the x-axis. So when we set our factored form of a function to zero we are finding the x-intercepts (zeroes of a graph). TLDR: x-values that satisfy 0=(x+a)(x-b)...=f(x) are my x-intercepts (my zeroes of a graph)
wow I actually get why factoring works now
Awesome!
or wait that's why they're the zeroes on the graph. So why does factoring work?
Factoring helps you find the zeroes on a graph. After you factor a function you have a bunch of (x+a)(x-b)... all multiplied together and equal to your function f(x).
So f(x)=(x+a)(x-b)...
Then we set the factored form to zero..... why? Well sort of because we can solve it easily using the zero product property. So when we set the factored form to zero
(x+a)=0
(x-b)=0
.
.
.
What are we doing? Well we are finding the x-values that make 0=(x+a)(x-b)...
Which is the same as finding when f(x)=0.
f(x)=0 is the x-axis. So when we set our factored form of a function to zero we are finding the x-intercepts (zeroes of a graph).
TLDR: x-values that satisfy 0=(x+a)(x-b)...=f(x) are my x-intercepts (my zeroes of a graph)