How do you factor the expression $$5x^3 - 7x^2$$ ?

To factor $$5x^3 - 7x^2$$ , you can take out the common factor, which is $$x^2$$ . The factored form is $$x^2(5x - 7)$$ .

What is the process to solve the equation $$2x^2 - 8x = 0$$ ?

To solve $$2x^2 - 8x = 0$$ , factor out the common term: $$2x(x - 4) = 0$$ . Then, set each factor to zero: $$2x = 0$$ (gives $$x = 0$$ ) and $$x - 4 = 0$$ (gives $$x = 4$$ ). Thus, the solutions are $$x = 0$$ or $$x = 4$$ .

What is the product of the expressions $$(x + 3)(x^2 - x + 4)$$ ?

The product of $$(x + 3)(x^2 - x + 4)$$ is $$x^3 + 2x^2 + x + 12$$ .

What is the degree of a polynomial?

The degree of a polynomial is the highest power of the variable in the expression. For example, in $$4x^3 + 2x^2 - x + 7$$ , the degree is 3.

How do you apply the Zero-Product Property to solve $$ (x - 11)(5x + 1) = 0 $$ ?

Set each factor to zero: $$x - 11 = 0$$ (gives $$x = 11$$ ) and $$5x + 1 = 0$$ (gives $$x = -\frac{1}{5}$$ ). Thus, the solutions are $$x = 11$$ or $$x = -\frac{1}{5}$$ .

What is the difference between a monomial and a polynomial?

A monomial is an algebraic expression with only one term, while a polynomial can have multiple terms. For example, $$3x$$ is a monomial, and $$3x + 2x^2 - 5$$ is a polynomial.

What is a factor of a polynomial?

A factor of a polynomial is an expression that divides the polynomial evenly, resulting in another polynomial. For example, $$(x - 2)$$ is a factor of $$x^2 - 2x + 4$$ .

What is the significance of the leading coefficient in a polynomial?

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the polynomial's graph.

How do you determine if a polynomial is prime?

A polynomial is considered prime if it cannot be factored into the product of two non-constant polynomials. For example, $$x^2 + 1$$ is prime.

What is the standard form of a polynomial?

The standard form of a polynomial is written in descending order of the degree of its terms. For example, $$4x^3 + 2x^2 - x + 7$$ is in standard form.

What is the relationship between the roots of a polynomial and its factors?

The roots of a polynomial are the values of the variable that make the polynomial equal to zero. Each root corresponds to a factor of the polynomial.

Algebraic Expressions and Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an algebraic expression?

Back

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It does not have an equality sign.

Tags

CCSS.6.EE.A.2B

2.

FLASHCARD QUESTION

Front

What is the Zero-Product Property?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.A.1

6.

FLASHCARD QUESTION

Front

What does it mean to factor an expression?

Back

Tags

CCSS.HSA.APR.C.4

7.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

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