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### Section 1.4 : Polynomials

1. Perform the indicated operation and identify the degree of the result.

Add $$4{x^3} - 2{x^2} + 1$$ to $$7{x^2} + 12x$$

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Here is the operation we’re being asked to perform.

$\left( {4{x^3} - 2{x^2} + 1} \right) + \left( {7{x^2} + 12x} \right)$

Note that the parenthesis are only there to illustrate how each polynomial is being used in the indicated operation and are not needed (or used) in general.

Here’s the result of the operation.

$\left( {4{x^3} - 2{x^2} + 1} \right) + \left( {7{x^2} + 12x} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{4{x^3} + 5{x^2} + 12x + 1}}$ Show Step 2

Remember the degree of a polynomial is just the largest exponent in the polynomial and so the degree of the result of this operation is three.