Factor And Remainder Theorem
Factor And Remainder Theorem
Value of a Polynomial:
The value of a polynomial f(x) at x = a is obtained by substituting the value of x= a in the given polynomial and it is denoted by f(a)
Illustration: Find the value of polynomial f(x) at x = 1, x= 1/2
Zero of a Polynomial:
The value of x for which the value of the polynomial becomes zero is called zero of polynomial.
Illustration: The value of the polynomial at x= 1
As f(1) is zero so x=1 is the zero of the polynomial
and (x-1) is a factor of this polynomial.
Factor and Remainder Theorem:
It states that:
For a polynomial p(x) of degree greater than of equal to one and 'a' be any real number. If p(x) is divided by the linear polynomial x-a then the remainder is p(a)
Illustration: Find the remainder when f(x) is divided by x-1
and the zero of x-1 is 1
So by the Remainder Theorem the remainder when f(x) is divided by x-1 is 2
Complete the following statements with an appropriate word/term to be filled in the blank spaces (s). x - a is a factors of the polynomial p(x), if p(a) = __________
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| Right Option : C | |||
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On dividing | |||
| Right Option : B | |||
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Find the remainder when | |||
| Right Option : D | |||
| View Explanation | |||
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