Question

Can anyone Help I have 25 questions, 2hr 40mins remaining,

Answer 1

Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:

$f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}$

How do we add polynomials?

We add polynomials combining the like-terms, that is, adding terms with the same exponent.

In this problem, the polynomials are:

• $f(x) = 3x^{\frac{1}{2}} + 7x^{-\frac{1}{4}} + 8x^{-4}$

• $g(x) = -\frac{7}{4}x^{\frac{1}{2}} + 12x^{-\frac{1}{4}} - 21x^3$

Combining the like terms, the addition is given by:

$f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3$

$f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}$

More can be learned about addition of polynomials at brainly.com/question/9438778

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