What is a quadratic polynomial?

A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form $$ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

What are the roots of a polynomial?

The roots of a polynomial are the values of the variable that make the polynomial equal to zero. For example, the roots of $$x^2 - 4 = 0$$ are $$x = 2$$ and $$x = -2$$ .

What is the leading coefficient of a polynomial?

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in the polynomial $$3x^4 + 2x^3 - x + 5$$ , the leading coefficient is 3.

What is a factor theorem?

The factor theorem states that if a polynomial $$f(x)$$ has a factor of the form $$(x - c)$$ , then $$f(c) = 0$$ . This means that $$c$$ is a root of the polynomial.

What is synthetic division?

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form $$(x - c)$$ . It is a quicker alternative to long division for polynomials.

What is the relationship between the degree of a polynomial and the number of roots?

The degree of a polynomial indicates the maximum number of roots it can have. For example, a polynomial of degree 3 can have up to 3 roots.

What is a complex root?

A complex root is a solution to a polynomial equation that includes imaginary numbers. For example, the roots of $$x^2 + 1 = 0$$ are $$x = i$$ and $$x = -i$$ .

What is the significance of the constant term in a polynomial?

The constant term in a polynomial is the value of the polynomial when the variable is zero. It can provide information about the polynomial's behavior and its graph.

Resource Library

Math

Algebra

Solving Polynomial Equations

Solving Polynomial Equations By Factoring 5th P

Solving Polynomial Equations by Factoring 5th P

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, HSA.APR.C.4, HSA.APR.B.2

Standards-aligned

Wayground Content

FREE Resource

Student preview

15 questions

Show all answers

FLASHCARD QUESTION

Front

What is a polynomial equation?

Back

FLASHCARD QUESTION

Front

What does it mean to factor a polynomial?

Back

FLASHCARD QUESTION

Front

What is the zero-product property?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

How do you solve a polynomial equation by factoring?

Back

To solve a polynomial equation by factoring, first factor the polynomial into simpler expressions, then apply the zero-product property to find the values of the variable that make each factor equal to zero.

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What is the difference of cubes formula?

Back

Tags

CCSS.HSA.APR.C.4

FLASHCARD QUESTION

Front

What is the sum of cubes formula?

Back

Tags

CCSS.HSA.APR.C.4

FLASHCARD QUESTION

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials with four or more terms by grouping terms in pairs and factoring out the common factors from each group.

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