Question

Use the √x button to create a polynomial that has 4 terms.

a) √x⁴ + √x³ + √x² + √x
b) √x³ + √x² + √x + √x⁴
c) √x² + √x + √x³ + √x⁴
d) √x⁴ + √x² + √x + √x³

Answer 1

All given options a), b), c), and d) simplify into a polynomial with four terms when the square roots are turned into fractional exponents. Hence, all the options are valid for creating a polynomial with 4 terms using the √x button.

Step-by-step explanation:

To create a polynomial with 4 terms using the √x button, we can consider each option given and simplify them. The √ symbol implies taking the square root, which is equivalent to raising a number to the power of 0.5. For example, √x⁴ means x⁴ raised to the power of 0.5, which simplifies to x² since (0.5 * 4 = 2). Similarly, √x³ is x raised to the power of 3/2, √x² simplifies to x, and √x simplifies to x to the power of 1/2 or x^0.5. Using that simplification method:

• Option a) √x⁴ + √x³ + √x² + √x simplifies to x² + x^(3/2) + x + x^(1/2)
• Option b) √x³ + √x² + √x + √x⁴ simplifies to x^(3/2) + x + x^(1/2) + x²
• Option c) √x² + √x + √x³ + √x⁴ simplifies to x + x^(1/2) + x^(3/2) + x²
• Option d) √x⁴ + √x² + √x + √x³ simplifies to x² + x + x^(1/2) + x^(3/2)

All options provide a polynomial with four terms, thus the question of creating one is simply a matter of arranging these terms in any sequence.