Rise Placement Test Exponents and Polynomials Questions and Answers

Question 1

Which of the following expressions is equivalent to (3x⁻⁴y⁵) / (x²y⁻²)?

Accepted Answer

3y⁷ / x⁶

Answer

To simplify the expression, use the quotient rule for exponents, which states that xᵃ/xᵇ = xᵃ⁻ᵇ. For the x terms: x⁻⁴ / x² = x⁻⁴⁻² = x⁻⁶. For the y terms: y⁵ / y⁻² = y⁵⁻⁽⁻²⁾ = y⁷. The expression becomes 3x⁻⁶y⁷. A negative exponent indicates a reciprocal, so x⁻⁶ moves to the denominator to become x⁶. The final simplified expression is 3y⁷ / x⁶.

Question 2

A rectangular park has a length of (4x + 5) meters and a width of (x - 2) meters. Which polynomial represents the total area of the park in square meters?

Accepted Answer

4x² - 3x - 10

Answer

The area of a rectangle is found by multiplying its length by its width. In this case, Area = (4x + 5)(x - 2). Use the FOIL method to multiply the binomials: First (4x * x = 4x²), Outer (4x * -2 = -8x), Inner (5 * x = 5x), Last (5 * -2 = -10). Combine the like terms: 4x² - 8x + 5x - 10 = 4x² - 3x - 10.

Question 3

Perform the subtraction: (8x² - 5x + 3) - (3x² + 2x - 7)

Accepted Answer

5x² - 7x + 10

Answer

To subtract the polynomials, distribute the negative sign to each term in the second polynomial: (8x² - 5x + 3) - 3x² - 2x + 7. Then, combine the like terms: (8x² - 3x²) + (-5x - 2x) + (3 + 7). This simplifies to 5x² - 7x + 10.

Question 4

Simplify the expression (2a³b⁻⁴)² completely.

Accepted Answer

4a⁶ / b⁸

Answer

To simplify, apply the outer exponent to each factor inside the parentheses. For the coefficient: 2² = 4. For the variables, use the power rule (xᵃ)ᵇ = xᵃᵇ. So, (a³)² = a³*² = a⁶, and (b⁻⁴)² = b⁻⁴*² = b⁻⁸. The expression becomes 4a⁶b⁻⁸. To express with only positive exponents, move the base with the negative exponent to the denominator, making the exponent positive. This results in 4a⁶ / b⁸.

Question 5

Which of the following is the correct factorization of the polynomial 9x² - 49?

Accepted Answer

(3x - 7)(3x + 7)

Answer

This polynomial is a difference of two squares, which follows the pattern a² - b² = (a - b)(a + b). In this case, a² is 9x², so a = 3x. And b² is 49, so b = 7. Applying the formula, the factorization is (3x - 7)(3x + 7).

Rise Placement Test Practice Test

Rise Placement Test Practice Test

Rise Placement Test Exponents and Polynomials Questions and Answers