Algebra Quiz: Simplification and Properties

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Questions and Answers

What is the value of the expression 21 × 10^(-3) when expressed in scientific notation?

2.1 × 10^(-3)

What is the factorization of the expression 8z^3 – 40z^2 + z – 5?

(8z^2 + 1)(z + 5)

What is the solution set of the equation (x^2 – 9)(x – 3) = 0?

{ -3,3}

What is the simplified form of the expression (2x – 3)(–5x^2 + 6x)?

-10x^3 + 27x^2 – 18x Signup and view all the answers

What is the value of x that satisfies the equation 4x + 14 = 26?

x = 3 Signup and view all the answers

What is the result of simplifying the expression (2𝑥 – 3)(5𝑥^2 + 6𝑥)?

10𝑥^3 – 27𝑥^2 – 18𝑥 Signup and view all the answers

Which of the following statements is true about the relationship between integers and rational numbers?

All integers are rational numbers, but not all rational numbers are integers. Signup and view all the answers

What is the key step in simplifying the expression (2𝑥 – 3)(5𝑥^2 + 6𝑥)?

Distributing the -3 to the terms inside the parentheses Signup and view all the answers

What is the purpose of simplifying expressions like (2𝑥 – 3)(5𝑥^2 + 6𝑥)?

To make the expression easier to work with Signup and view all the answers

What is the mistake in the simplification of the expression (2𝑥 – 3)(5𝑥^2 + 6𝑥) if the result is 10𝑥^3 + 3𝑥^2 – 18𝑥?

The distribution of the -3 is incorrect Signup and view all the answers

What is the simplified result of the expression (2𝑥 3 + 4𝑥 2 + 7𝑥 – 3) – (4𝑥 2 + 3𝑥 + 6)?

2𝑥 3 + 4𝑥 – 9 Signup and view all the answers

What is the difference between the two expressions (2𝑥 3 + 4𝑥 2 + 7𝑥 – 3) and (4𝑥 2 + 3𝑥 + 6)?

A polynomial with a degree of 3 Signup and view all the answers

What type of numbers are whole numbers a subset of?

Real numbers Signup and view all the answers

What is the relationship between integers and whole numbers?

Whole numbers are a subset of integers Signup and view all the answers

What is the term for the highest degree of a polynomial expression?

Degree Signup and view all the answers

What is the degree of the polynomial (2x^2 + 3x)^2?

4 Signup and view all the answers

What is the Greatest Common Factor (GCF) of 8x^2 and 10y^4?

2x^2 Signup and view all the answers

Is the point (2, –1) a solution to the equation 3[2(y – 1) + 2x] – 2y = –4?

Yes, it is a solution. Signup and view all the answers

Is the polynomial x^2 + x + 1 prime?

Yes, it is prime. Signup and view all the answers

What is the result of expanding the expression (2x^2 + 3x)^2?

4x^4 + 12x^3 + 9x^2 Signup and view all the answers

Which of the following statements is true about natural numbers and integers?

All natural numbers are integers, but not all integers are natural numbers. Signup and view all the answers

What is the condition for y in the expression of a rational number 𝑥 𝑦?

y is an integer and y ≠ 0 Signup and view all the answers

Which of the following is a characteristic of a rational number?

It can be expressed as a fraction with integer numerator and denominator Signup and view all the answers

What is the relationship between the numerator and denominator in a rational number?

The numerator and denominator are integers Signup and view all the answers

Which of the following is NOT a characteristic of a rational number?

It can be expressed as a percentage Signup and view all the answers

Study Notes

Simplifying Expressions

(2𝑥 – 3)(5𝑥² + 6𝑥) simplifies to 10𝑥³ – 27𝑥² – 18𝑥
(2𝑥 ² + 3𝑥)² has a degree of 4

Polynomials and Factoring

The GCF of 8𝑥² and 10𝑦⁴ is 2𝑥²
8𝑧³ – 40𝑧² + 𝑧 – 5 factors to (8𝑧² + 1)(𝑧 – 5)

Equations and Inequalities

The solution set of (𝑥² – 9)(𝑥 – 3) = 0 is { – 3,3}
The equation 4𝑥 + 14 = 26 solves to 𝑥 = 3
The y-intercept of 10𝑥 + 8𝑦 = 40 is (0,5)

Properties of Numbers

Not all integers are rational numbers
All integers are whole numbers
A rational number is a number that can be written as 𝑥/𝑦 where x, y are integers and 𝑦 ≠ 0

Geometry and Graphing

The point (2, – 1) is a solution to the equation 3[ 2(y – 1) + 2x] – 2y = – 4
Where 𝑥 < 0, the point ( – 𝑥, – 2) is located in the III quadrant

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