By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = 4x³ - 12x² + 14x - 3, g(x) = 2x - 1
Solution:
Given, p(x) = 4x³ - 12x² + 14x - 3
g(x) = 2x - 1
We have to find the remainder by remainder theorem when p(x) is divided by g(x).
The remainder theorem states that when a polynomial f(x) is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a).
Let g(x) = 0
2x - 1 = 0
2x = 1
x = 1/2
Substitute x = 1/2 in p(x) to get the remainder,
p(3) = 4(1/2)³ - 12(1/2)² + 14(1/2) - 3
= 4(1/8) - 12(1/4) + 14/2 - 3
= 1/2 - 3 + 7 - 3
= 1/2 + 7 - 6
= 1/2 + 1
= 3/2
Therefore, the remainder is 3/2.
✦ Try This: By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x³ - 6x² - x - 3, g(x) = x + 1
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 14(iii)
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = 4x³ - 12x² + 14x - 3, g(x) = 2x - 1
Summary:
By Remainder Theorem the remainder, when p(x) is divided by g(x), where p(x) = 4x³ - 12x² + 14x - 3, g(x) = 2x - 1 is 3/2
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