12) What is the degree of the resulting polynomial when a 3rd degree binomial is added to a 4th degree trinomial?

Since adding polynomials doesn't change the degree (unless the two highest degree terms match and cancel each other out), the result will just be the degree of the highest degree polynomial.

In your case, the result will be a 4th degree polynomial.

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step-by-step explanation:

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus