Factoring Problem...Please Help

[Samara]

This is just a practice test, not homework, or anything for a grade...I am simply trying to figure out how this problem is done...I know what the answer is (it is highlighted), I just need help learning the process.

Any help would greatly be appreciated!

Thank you!

 

[Deleted member 4993]

View attachment 1603

This is just a practice test, not homework, or anything for a grade...I am simply trying to figure out how this problem is done...I know what the answer is (it is highlighted), I just need help learning the process.

Any help would greatly be appreciated!

Thank you!

First factor out 7

28x⁴ - 63 = 7 * [4x⁴ - 9] = 7 * [(2x²)² - 3²] = 7 * [2x² + 3] * [2x² - 3]

We have used the following property for the last step:

a² - b² = (a+b)*(a-b)

 

[srmichael]

28x^4 - 63

Problem statement says "factor" (nothing else);
if this was part of a timed test and you had a minute to go,
wonder if you'd get full marks for:
[SQRT(28)x^2 + SQRT(63)][SQRT(28)x^2 - SQRT(63)]

Opinions?

Depends on the teacher, I guess. Yes, that is technically factored, but most teachers want the "a" and "b" or a^2 - b^2 to be perfect squares. Every kid that I have tutored over the many years have had teachers that want "a" and "b" to be perfect squares before you can utilize the (a + b)(a - b) factoring.

 

[lookagain]

28x^4 - 63

Problem statement says "factor" (nothing else);
if this was part of a timed test and you had a minute to go,
wonder if you'd get full marks for:
[SQRT(28)x^2 + SQRT(63)][SQRT(28)x^2 - SQRT(63)]

Opinions?

"Factor completely" means to factor completely over the integers,

unless there are additional requirements (such as over the Complex numbers).

 

[Samara]

Thank you very much for your help! I understand it much much better now!