What is the Factor Theorem?

The Factor Theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0.

What is the Remainder Theorem?

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

What is the process of factoring by grouping?

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor it into simpler polynomials.

What is a root of a polynomial?

A root of a polynomial is a value of x that makes the polynomial equal to zero.

What is the quadratic formula?

The quadratic formula is $$x = \frac{{-b \text{±} \text{sqrt}(b^2 - 4ac)}}{{2a}}$$ for solving quadratic equations.

What is the significance of the discriminant in a quadratic equation?

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction.

What is the definition of a complex number?

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Test #10 - Algebra 3 Flashcards: 15 Cards (12th Grade)

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What are the roots of the polynomial equation $x^3 - 10x^2 + 19x + 30 = 0$ ?

Back

The roots are -1, 6, and 5.

2.

FLASHCARD QUESTION

Front

What are the roots of the polynomial equation $x^3 - 2x^2 - 21x - 18 = 0$ ?

Back

The roots are 6, -3, and -1.

3.

FLASHCARD QUESTION

Front

Solve by factoring: $4x^2 + 11x - 3 = 0$

Back

The solutions are x = 1/4 and x = -3.

4.

FLASHCARD QUESTION

Front

How do you solve $20x^3 - 25x^2 + 4x - 5$ by factoring by grouping?

Back

The solutions are x = -5/4 and $\frac{i\text{sqrt}{5}}{5}$ .

5.

FLASHCARD QUESTION

Front

Simplify the expression: -15 + 8√9

Back

The simplified expression is 9 + 14√3.

6.

FLASHCARD QUESTION

Front

What is the definition of a polynomial?

Back

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

7.

FLASHCARD QUESTION

Front

What is the degree of the polynomial $x^3 - 10x^2 + 19x + 30$ ?

Back

The degree is 3.

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