Is Expanding (x - a)^4 Necessary for Factoring 64(x - a)^4 - x + a?

  • MHB
  • Thread starter mathdad
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In summary, the degree of the polynomial is 4 because it is the highest power that appears in the expression. There are two terms in this polynomial: 64(x - a)^4 and -x + a. The leading coefficient is 64 because it is the coefficient of the term with the highest power. The constant term is a because it is the term without a variable. This polynomial can be factored as (x - a)(64(x - a)^3 - 1).
  • #1
mathdad
1,283
1
Factor: 64(x - a)^4 - x + a

Must I expand (x - a)^4 as step 1?
 
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  • #2
As a first step, I would write:

\(\displaystyle 64(x-a)^4-x+a=64(x-a)^4-(x-a)\)

Next factor out $x-a$, and the other factor will be the difference of cubes. :D
 
  • #3
I can take it from here.
 

FAQ: Is Expanding (x - a)^4 Necessary for Factoring 64(x - a)^4 - x + a?

What is the degree of the polynomial?

The degree of this polynomial is 4 because it is the highest power that appears in the expression.

How many terms are in the polynomial?

There are two terms in this polynomial: 64(x - a)^4 and -x + a.

What is the leading coefficient?

The leading coefficient is 64 because it is the coefficient of the term with the highest power.

What is the constant term?

The constant term is a because it is the term without a variable.

How can this polynomial be factored?

This polynomial can be factored as (x - a)(64(x - a)^3 - 1).

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