Question

Which of the following is a factor of m⁴ - 256 ?
1 point
m + 4,
m² - 4,
m + 16,
m² + 4​

Answer 1

Identity used : a² - b² = (a+b)(a-b)

m⁴ - 256

(m²)² - (16)²

(m² + 16)(m² - 16)

(m² + 16)(m + 4)(m - 4)

As you see three factor come up for this equation and (m + 4) is the answer for above question

Answer 2

Explanation:

We have to find factor of m^4-256

=>(m^2)^2-(16)^2(We can expand the question in this way,now consider m^2 = a & 16=b,if we clearly observe,we can see an identity i.e. a^2-b^2=(a+b)(a-b).)

=>(m^2+16)(m^2-16)

=>(m^2+16)[(m)^2-(4)^2]

(Now,we can expand m^2-16 as (m)^2-(4)^2 ,here,consider m=a & 4=b,if we clearly observe,we can see an identity i.e. a^2-b^2=(a+b)(a-b).)

=>(m^2+16)(m+4)(m-4)

These are the factors of m^4-256.

In the options,only m+4 is given which matches our answer.

Therefore,m+4 ans.