Page 155 - Algebra

We know that,
Dividend = Divisor × Quotient + Remainder
If p(x) is the quotient
Dividend = (x –a) p(x) + f(a)
Factor theorem
A polynomial function f(x) will have (x –a) as a factor when f(a) = 0
REMEMBER:
For a polynomial function f(x) and a real number a
• • • • • •
a is a solution of f(x) = 0
a is the root of f(x)
a is the zero of f(x)
x – a is a factor of f(x)
a is the intercept of f(x)
f(x) is divisible by (x – a)
Worked Example
Find the remainder when f(x) = 2x4 – 5x2 + 2x – 13 is divided by x – 2
Solution:
Here x – a = x – 2
a =2
To find the remainder, put f(a) in the function. So, f(2) = 2(2)4 – 5(2)2 + 2(2) – 13
= 32 – 20 + 4 – 13 = 3
Page 154 of 177
Algebra I & II