Question

When adding polynomials are the exponents always added together?

Answer 1

No

Explanation:

Exponents are only added when polynomials are multiplied and only applies to like terms. You add the coefficients of the like terms instead.

For example:

`(x^2+3x+6)+(2x^2-4x+1)=(1+2)x^2-(3-4)x+(6+1)=3x^2-x+7`

Answer 2

no

Explanation:

The exponents are added when the the same coefficient is multiplied:

`x^2(x^3) = x^5`

If you think about it:

x^2 = x * x and x^3 = x * x * x

so you get:

(x^2)(x^3) = x * x * x * x * x = x^5

But, when adding x's of the same power, you add a coefficient:

`x^2 + x^2 = 2x^2`, not
`x^2 + x^2 = x^4`

Always remember to only add exponents when the coefficient/variable is multiplied, not added.

And, when an exponent is put to an exponent, multiply them:

`(x^3)^3 = x^3^(^3^) = x^9`