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Questions and Answers
Which expression represents the application of the distributive law correctly?
Which expression represents the application of the distributive law correctly?
What is the result of factoring the expression $6x^2 + 9x$?
What is the result of factoring the expression $6x^2 + 9x$?
If $x = 3$ and $y = -4$, what is the value of the expression $3x + 2y$?
If $x = 3$ and $y = -4$, what is the value of the expression $3x + 2y$?
Which statement correctly describes the outcome of dividing the polynomial $2x^3 + 4x^2$ by $2x$?
Which statement correctly describes the outcome of dividing the polynomial $2x^3 + 4x^2$ by $2x$?
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What is the result of adding $(-5)$ and $12$?
What is the result of adding $(-5)$ and $12$?
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Study Notes
Distributive Law
- The distributive law states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
- For example, the expression $3(x + 2)$ can be expanded using the distributive law as $3x + 6$.
Factoring Expressions
- To factor an expression, you need to find the greatest common factor (GCF) of the terms in the expression.
- The GCF is the largest number or variable that divides into all of the terms.
- In the expression $6x^2 + 9x$, the GCF is $3x$.
- By factoring out the GCF, we get the expression $3x(2x + 3)$.
Evaluating Expressions
- To evaluate an expression, you need to substitute the given values for the variables.
- In the expression $3x + 2y$, substituting $x = 3$ and $y = -4$ gives us: $3(3) + 2(-4) = 9 - 8 = 1$.
Polynomial Division
- Dividing a polynomial by a monomial involves dividing each term of the polynomial by the monomial.
- For example, dividing $2x^3 + 4x^2$ by $2x$ results in:
- $(2x^3) / (2x) = x^2$
- $(4x^2) / (2x) = 2x$
- Therefore, the result is $x^2 + 2x$.
Adding Integers
- Adding a negative integer is the same as subtracting the absolute value of the integer.
- Adding $(-5)$ and $12$ is equivalent to $12 - 5$, which equals $7$.
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Description
Test your understanding of the distributive law and factoring in algebra. This quiz covers various algebraic expressions and their evaluations, including polynomial division and simple arithmetic. Challenge yourself with these essential algebra concepts!
