Polynomial Remainders
Lesson · Intermediate
Algebra: Polynomials
Find the remainder when
is divided by
Non-efficient way: Long Division
and we don't need to know the quotient
Efficient way: Set the divisor equal to 0
Find the remainder when
is divided by
Don't say \(x=\pm1\), the remainder can have \(x\) since
Find the remainder when
is divided by
Find the remainder when
is divided by
APPROACH 1
APPROACH 2
\(A(x)\) is a polynomial that when divided by \(x+1\) and \(x-1\), the remainders are \(-2\) and \(5\), respectively. Find the remainder when \(A(x)\) is divided by \(x^2-1\)
When divided by
For finding the remainder
Only use \(x^2=1\), don't use \(x=\pm1\)
\(R(x)\) can have \(x\), use \(x^2=1\) for powers of \(x\) that are at least 2