Factor Theorem for Polynomials
Read this topicExplanations 4
- Just as how we can factor numbers (for example, 12=22⋅312=2^2\cdot 312=22⋅3), we can also factor polynomials by decomposing it into a product of one or more smaller polynomials.…
By Steven Kwon, Victor Wang, Matt Superdock, Tim Ratigan, Alexander Mason, Anusha Rahman
- The Factor Theorem states that the expression x−ax-ax−a, where aaa is a constant, is a factor of a polynomial p(x)p(x)p(x) if and only if p(a)=0p(a)=0p(a)=0. How can we begin to…
By Anand Iyer, Anusha Rahman
- (Video) Factoring Polynomials Using Factor Theorem by MrsALovesMath This video by MrsALovesMath walks through an example of using factor theorem to factor polynomials. Summary W…
By Anusha Rahman
- Factor Theorem An extension of the Remainder Theorem is the Factor Theorem! The Factor Theorem tells us that, for any polynomial f(x)f(x)f(x),: If f(a)=0f(a)=0f(a)=0, then (x−a)…
By Anusha Rahman
Problems 4
- Find the sum of all positive integers 1≤k≤991\leq k\leq 991≤k≤99 such that there exist positive integers aaa and bbb with the property that x100−axk+b=(x2−2x+1)P(x)x^{100}-ax^k+…
- How would you use the factor theorem to determine if x−1x-1x−1 is a factor of 2x4+3x2–5x+72x^4 + 3x^2 – 5x + 72x4+3x2–5x+7?
- Let fff be a polynomial such that f(0)=1f(0) = 1f(0)=1 and f(1)=f(2)=0f(1) = f(2) = 0f(1)=f(2)=0. Which of the following are possible degrees of fff?
- Let fff be a polynomial such that f(0)=0f(0) = 0f(0)=0 and f(1)=f(2)=f(3)=1f(1) = f(2) = f(3) = 1f(1)=f(2)=f(3)=1. Which of the following are possible degrees of fff?