Factoring Help PLEASE!!

[Datdudedak]

[SIZE=-1]Factor the following completely: x^2 + 64
Factor the following completely: mx − my + px − py
Factor the following completely: x^2 + 6x + 5
Factor the following completely: x^2 − x − 30
Factor the following completely: x^2 + 3x − 10
Help is much appreciated! Thank You! [/SIZE]

 

[lookagain]

[SIZE=-1]Factor the following completely: x^2 + 64
Factor the following completely: mx − my + px − py
Factor the following completely: x^2 + 6x + 5
Factor the following completely: x^2 − x − 30
Factor the following completely: x^2 + 3x − 10
Help is much appreciated! Thank You! [/SIZE]

Please show all of your work/attempts first for us to know where you're stuck.

 

[mmm4444bot]

Factor the following completely: x^2 + 64

A sum of squares does not factor, unless you use some imaginary coefficients.

I'm guessing that you're supposed to stick with Real numbers.

Did the instructions specify "factor if possible" ?

Or, maybe there is a typographical error, and it should be x^2 - 64, instead.

(There is a famous factoring pattern for a difference of squares.)

Factor the following completely: mx − my + px − py
Factor the following completely: x^2 + 6x + 5
Factor the following completely: x^2 − x − 30
Factor the following completely: x^2 + 3x − 10

Factor by grouping, on the first one quoted above.

On the last three exercises, you could start by finding:

two numbers (let's call them a and b) whose product is 5 and whose sum is 6

two numbers whose product is -30 and whose sum is -1

two numbers whose product is -10 and whose sum is 3

Then, the factoring takes the form (x + a)(x + b).

Can you make a start?