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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Polynomials - Algebra Study Guide</title>
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</head>
<body>
<header>
<h1>Polynomials</h1>
</header>
<nav>
<a href="algebra.html">Back to Algebra</a>
<a href="index.html">Back to Study Guide</a>
</nav>
<div class="container">
<h2>What is a Polynomial?</h2>
<p>A <strong>polynomial</strong> is an expression consisting of variables (also called indeterminates) raised to various powers, combined using addition, subtraction, and multiplication. The general form of a polynomial is:</p>
<pre>p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀</pre>
<p>Where the <b>aₙ, aₙ₋₁, ..., a₀</b> are constants (called coefficients), and <b>x</b> is the variable. The exponent (n) is a non-negative integer.</p>
<h3>Operations with Polynomials:</h3>
<div class="step">
<i class="fas fa-plus"></i>
<div>
<h4>1. Addition</h4>
<p>To add polynomials, combine like terms (terms that have the same variable raised to the same power).</p>
</div>
</div>
<div class="step">
<i class="fas fa-minus"></i>
<div>
<h4>2. Subtraction</h4>
<p>To subtract polynomials, distribute the negative sign and combine like terms.</p>
</div>
</div>
<div class="step">
<i class="fas fa-times"></i>
<div>
<h4>3. Multiplication</h4>
<p>To multiply polynomials, use the distributive property (multiply each term in the first polynomial by each term in the second polynomial).</p>
</div>
</div>
<h3>Example 1: Polynomial Addition</h3>
<div class="example-box">
<p><strong>Add the polynomials <code>2x² + 3x + 4</code> and <code>x² - x + 1</code>:</strong></p>
<pre>
(2x² + 3x + 4) + (x² - x + 1) = (2x² + x²) + (3x - x) + (4 + 1)
= 3x² + 2x + 5
</pre>
</div>
<h3>Example 2: Polynomial Subtraction</h3>
<div class="example-box">
<p><strong>Subtract <code>(3x² + 4x - 2)</code> from <code>(5x² - 2x + 7)</code>:</strong></p>
<pre>
(5x² - 2x + 7) - (3x² + 4x - 2) = (5x² - 3x²) + (-2x - 4x) + (7 + 2)
= 2x² - 6x + 9
</pre>
</div>
<h3>Example 3: Polynomial Multiplication</h3>
<div class="example-box">
<p><strong>Multiply <code>(x + 2)</code> and <code>(x - 3)</code>:</strong></p>
<pre>
(x + 2)(x - 3) = x² - 3x + 2x - 6
= x² - x - 6
</pre>
</div>
<h3>Try Solving It Yourself:</h3>
<p>Now, try adding and subtracting these polynomials:</p>
<pre>2x³ + x² - 3x + 5 and x³ + 4x² - x - 1</pre>
<a href="#" class="button">Click here for the solution</a>
</div>
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