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Define remainder theorem nd factor theorem?
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Define remainder theorem nd factor theorem?
The Remainder Theorem:
When we divide a polynomial f(x) by x−c the remainder is f(c)
The Factor Theorem:
When f(c)=0 then x−c is a factor of f(x)
And the other way around, too:
When x−c is a factor of f(x) then f(c)=0
When we divide a polynomial f(x) by x−c the remainder is f(c)
The Factor Theorem:
When f(c)=0 then x−c is a factor of f(x)
And the other way around, too:
When x−c is a factor of f(x) then f(c)=0
Community Answer
Define remainder theorem nd factor theorem?
Answer:
The two theorems are similar, but refer to different things.
Explanation:
The
remainder theorem
tells us that for any polynomial f
(
x
)
x
−
a
f
(
a
)
The
factor theorem
tells us that if a
f
(
x
)
(
x
−
a
)
f
(
x
)
For example, let's consider the polynomial
f
(
x
)
=
x
2
−
2
x
+
1
Using the remainder theorem
We can plug in
3
f
(
x
)
f
(
3
)
=
3
2
−
2
(
3
)
+
1
f
(
3
)
=
9
−
6
+
1
f
(
3
)
=
4
Therefore, by the remainder theorem, the remainder when you divide
x
2
−
2
x
+
1
x
−
3
4
You can also apply this in reverse. Divide
x
2
−
2
x
+
1
x
−
3
f
(
3
)
Using the factor theorem
The quadratic polynomial
This tells us that
f
(
x
)
=
x
2
−
2
x
+
1
0
x
=
1
This tells us that
(
x
−
1
)
x
2
−
2
x
+
1
We can also apply the factor theorem in reverse:
We can factor
x
2
−
2
x
+
1
(
x
−
1
)
2
1
f
(
x
)
Basically, the remainder theorem links the remainder of division by a binomial with the value of a function at a point, while the factor theorem links the factors of a polynomial to its
zeros.
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Define remainder theorem nd factor theorem?
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Define remainder theorem nd factor theorem? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Define remainder theorem nd factor theorem? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Define remainder theorem nd factor theorem?.
Define remainder theorem nd factor theorem? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Define remainder theorem nd factor theorem? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Define remainder theorem nd factor theorem?.
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