Can I simplify these ?

Question

1. x^3-36x

2. x^2+x

Oh and How do I factor this 2x^2+x-15?

please explain what you did it would help me to comprehend how to this in the future!

Regards,

LAFONTAINE

Answer 1

Okay:

#1) x^3 - 36x
-You immediately notice that there's an x variable in both terms so you can definitely bring that out like so:
x (x^2 - 36)

(x^2 - 36) can be factored:
(x - 6) (x + 6)

So your answer is: x (x - 6)(x + 6)

If you want to check your answer you can multiply everything back and you should get your original equation:
x(x - 6)(x + 6)
= x(x^2 + 6x - 6x - 36)
=x(x^2 - 36)
=x^3 - 36x (GREAT!! you got the original function back) :)

#2) x^2 + x
-Again, you notice that x is in both terms and you can bring that out:
x^2 + x
= x(x+1)

#3) 2x^2+x-15
-In this equation we won't be able to bring the variable "x" out because it isn't in every term (meaning although it's present with 2x^2 and x, it isn't present in 15)
-So in this case you just factor like so:
2x^2 + x - 15
= (2x - 5)(x + 3 )

You can also check to see if your answer is correct again by multiplying the values within the two parentheses to see if you get back the original function:

(2x - 5)(x + 3)
-First, multiple the 1st term in each parentheses: 2x*2
-Then, multiply the 1st term in the first parenthese by the 2nd term in the second parenthese: 2x*3 = 6x
-Now, multiply the 2nd term in the first parenthese by the 1st term in the second parenthese: -5*x = -5x
-Finally, multiply the 2nd term in the first parenthese by the 2nd term in the second parenthese: -5*3 = -15

Put all these together: 2x^2 + 6x -5x -15
-Add like terms: 2x^2 + x - 15 (YAY! This is the original equation!) :)

I hope this helps you!

Good luck!

Love,
Mary

Answer 2

1. x^3-36
= x (x^2-36)
= x (x+6) (x-6)

2. x^2+x
= x (x+1)

3. 2x^2+x-15
= (2x - 5)(x+ 3)

When factoring the sum of the product of the outer components and the product of the inner components is equal to the middle factor.

Answer 3

1st question:
= x^3 - 36x
= x(x^2 - 36)
= x (x - 6) (x + 6)

2nd question:
= x^2 + x
= x (x + 1)