What is the process for subtracting polynomials?

To subtract polynomials, distribute the negative sign and then combine like terms. For example, $$(5x^2 + 3) - (2x^2 + 4) = 3x^2 - 1$$ .

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 ≠ 0.

How do you factor a quadratic polynomial?

To factor a quadratic polynomial of the form $$ax^2 + bx + c$$ , find two numbers that multiply to ac and add to b. For example, $$x^2 + 5x + 6$$ factors to $$(x + 2)(x + 3)$$ .

What is the remainder theorem?

The remainder theorem states that if a polynomial $$f(x)$$ is divided by $$(x - c)$$ , the remainder is $$f(c)$$ .

What is the difference of squares?

The difference of squares is a special factorization pattern given by $$a^2 - b^2 = (a - b)(a + b)$$ .

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, $$3x^4 + 2x^3 - x + 5$$ is in standard form.

How do you evaluate a polynomial at a given value?

To evaluate a polynomial at a given value, substitute the value for the variable and simplify. For example, to evaluate $$2x^2 + 3x - 5$$ at $$x = 2$$ , calculate $$2(2)^2 + 3(2) - 5 = 3$$ .

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 determines the end behavior of the polynomial's graph.

UGHS Honors Geometry Unit 1 Study Guide Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

What is a constant term in a polynomial?

Back

4.

FLASHCARD QUESTION

Front

How do you find the coefficient of a term in a polynomial?

Back

5.

FLASHCARD QUESTION

Front

What is the formula for the perimeter of a rectangle?

Back

6.

FLASHCARD QUESTION

Front

What is the difference between a monomial and a polynomial?

Back

7.

FLASHCARD QUESTION

Front

How do you add polynomials?

Back

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