find the remainder when x⁴+ x³-2x²+ x + 1 is divided by x-1
Answers
p(x) = x⁴+ x³-2x²+ x + 1
By Remainder Theorem :
x - 1 = 0
x = 1
p(x) = x⁴+ x³-2x²+ x + 1
p(1) = (1)⁴ + (1)³ - 2(1)² + (1) +1
p(1) = 1 + 1 - 2 + 1
p(1) = 3 - 2
p(1) = 1
Remainder = 1
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The remainder is 2; when x⁴+ x³-2x²+ x + 1 is divided by x-1.
Given:
- Two polynomials.
- x⁴+ x³-2x²+ x + 1
- x-1
To find:
- Find the remainder when x⁴+ x³-2x²+ x + 1 is divided by x-1.
Solution:
Theorem\Concept to be used:
Remainder Theorem: When a polynomial p(x) is divided by x-a, then remainder is given by p(a); i.e. value of polynomial at x=a.
Step 1:
Find value of x from x-1.
So,
Thus,
Step 2:
Put the value of x in p(x).
Let
or
or
Thus,
Remainder is 2, when x⁴+ x³-2x²+ x + 1 is divided by x-1.
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