Mathematics

Mathematics

Problem

Consider the expression r(x)=12x5−3x3+2x2−12x5+4.r(x)=\frac{1}{2}x^{5}-3x^{3}+2x^{2}-\frac{1}{2}x^{5}+4. Answer the following questions. a. (i) Simplify r(x)r(x) by combining like terms. b. (ii) For the simplified form of r(x)r(x), write down: (a) its degree, (b) the leading coefficient, (c) the constant term. c. (iii) State whether the simplified polynomial is a monomial, binomial, trinomial or has more than three terms.
Intuitive explanation

Start by combining like terms—this polynomial looks messier than it is. Notice that the x5x^5 terms will partially cancel, leaving you with a simpler expression to work with. Once you've collected all terms of the same degree, you'll have a cleaner function that's much easier to analyze, differentiate, or evaluate depending on what comes next.

Intuitive explanation

Start by combining like terms—this polynomial looks messier than it is. Notice that the x5x^5 terms will partially cancel, leaving you with a simpler expression to work with. Once you've collected all terms of the same degree, you'll have a cleaner function that's much easier to analyze, differentiate, or evaluate depending on what comes next.

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