What is the value of k for which (a-3b) is a factor of a4 - 7a2b2 + kb4?

In summary, the Remainder Theorem and the Factor Theorem are mathematical concepts that involve using the roots of a polynomial to determine its properties. The Remainder Theorem is used to find the remainder when a polynomial is divided by another polynomial, while the Factor Theorem is used to determine the factors of a polynomial. Both theorems rely on the same concept of using the roots of a polynomial to simplify mathematical operations.
  • #1
electrofanner
5
0
Find the value of k for which (a-3b) is a factor of a4 - 7a2b2 + kb4.

Hence, for this value of k, factorize a4 - 7a2b2 + kb4 completely.

I tried to do it but my mind is not going anywhere.

Any help will be greatly appreciated. :)
 
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  • #2
To find the value of k you'll need to do polynomial division.
 
  • #3
If (a-3b) is a factor of a4 - 7a2b2 + kb4,
then if you plug in 3b for a, you should get zero.
 
  • #4
Excellent idea, SammyS!
 

FAQ: What is the value of k for which (a-3b) is a factor of a4 - 7a2b2 + kb4?

1. What is the Remainder Theorem?

The Remainder Theorem is a mathematical concept that states that when a polynomial f(x) is divided by another polynomial g(x), the remainder is equal to f(c), where c is the value of the variable x at which the division is carried out.

2. How is the Remainder Theorem used?

The Remainder Theorem is used to find the remainder when a polynomial is divided by another polynomial. It is especially useful in polynomial long division, where it allows us to simplify the process by reducing the number of terms in the dividend.

3. What is the Factor Theorem?

The Factor Theorem is a mathematical concept that states that if a polynomial f(x) has a root at x=c, then (x-c) is a factor of f(x). In other words, if the remainder when f(x) is divided by (x-c) is equal to 0, then (x-c) is a factor of f(x).

4. How is the Factor Theorem used?

The Factor Theorem is used to determine the factors of a polynomial. By finding the roots of a polynomial and using the Factor Theorem, we can factorize the polynomial into its individual factors, making it easier to solve equations and perform other mathematical operations.

5. What is the difference between the Remainder Theorem and the Factor Theorem?

The main difference between the Remainder Theorem and the Factor Theorem is that the Remainder Theorem deals with finding the remainder when a polynomial is divided by another polynomial, while the Factor Theorem deals with finding the factors of a polynomial. However, both theorems rely on the same concept of using the roots of a polynomial to determine its properties.

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