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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?
- $a(b - c) = ab + ac$
- $a(b + c) = ab - ac$
- $a(b - c) = ab - ac$
- $a(b + c) = ab + ac$ (correct)
What is the result of factoring the expression $6x^2 + 9x$?
What is the result of factoring the expression $6x^2 + 9x$?
- $3(x(2x + 3))$
- $9(x + 2/3)$
- $3x(2x + 3)$ (correct)
- $6x(x + 1.5)$
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 $3x + 2y$?
- $7$
- $-6$ (correct)
- $-7$
- $-5$
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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