Best Practices Flashcards

When simplifying the expression (3x²)(4x³), what is the correct result?

Answer: 12x⁵

Multiply coefficients (3×4=12) and add exponents (2+3=5) to get 12x⁵.

What is the best first step when solving the equation 2(x + 5) = 18?

Answer: Distribute the 2 to get 2x + 10 = 18

Distributing first gives 2x + 10 = 18, which is easiest to solve by then subtracting 10.

A student writes √(a² + b²) = a + b. This is incorrect because:

Answer: Square roots do not distribute over addition

√(a² + b²) ≠ a + b; the Pythagorean theorem shows the correct form is c = √(a² + b²).

Which strategy is most efficient for finding the vertex of f(x) = x² − 6x + 8?

Answer: Complete the square or use x = −b/(2a)

Using the vertex formula x = −b/(2a) = 3 gives the x-coordinate of the vertex quickly.

Before adding the fractions 2/x + 3/(x+1), the best practice is to:

Answer: Find a common denominator of x(x+1)

A common denominator x(x+1) allows the fractions to be rewritten before adding numerators.

When checking a solution to a radical equation like √(x+3) = x−1, you should always:

Answer: Substitute the solution back into the original equation

Squaring can introduce extraneous solutions, so substituting back into the original equation is essential.

When dividing both sides of an inequality by −3, you must:

Answer: Reverse the inequality sign

Dividing or multiplying an inequality by a negative number reverses the direction of the inequality.