How do you factor the polynomial $$a^2 + 15a + 44$$ ?

To factor $$a^2 + 15a + 44$$ , look for two numbers that multiply to 44 and add to 15. The factors are 11 and 4, so it can be factored as $$(a + 11)(a + 4)$$ .

What is the result of dividing $$a^2 + 15a + 44$$ by $$a + 4$$ ?

Using synthetic division or polynomial long division, the result is $$a + 11$$ with a remainder of 0.

What is long division of polynomials?

Long division of polynomials is a method similar to long division with numbers, where you divide the leading term of the dividend by the leading term of the divisor, multiply, and subtract.

What is a zero of a polynomial?

A zero of a polynomial is a value of $$x$$ for which the polynomial evaluates to zero. For example, if $$f(x) = x^2 - 4$$ , then the zeros are $$x = 2$$ and $$x = -2$$ .

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.

What is the difference between a monomial, binomial, and trinomial?

A monomial has one term (e.g., $$3x$$ ), a binomial has two terms (e.g., $$x + 2$$ ), and a trinomial has three terms (e.g., $$x^2 + 3x + 4$$ ).

How do you check if a polynomial is divisible by another polynomial?

To check if a polynomial $$f(x)$$ is divisible by another polynomial $$g(x)$$ , perform polynomial long division. If the remainder is zero, then $$f(x)$$ is divisible by $$g(x)$$ .

What is the purpose of factoring polynomials?

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in finding the roots or zeros of the polynomial.

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

The roots of a polynomial are the values of $$x$$ that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial in the form $$(x - r)$$ , where $$r$$ is a root.

Dividing Polynomials Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to divide polynomials?

Back

Dividing polynomials involves finding how many times one polynomial (the divisor) can fit into another polynomial (the dividend), resulting in a quotient and possibly a remainder.

Tags

CCSS.HSA.APR.D.6

3.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Tags

CCSS.HSA.APR.D.6

5.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

Tags

CCSS.HSA.APR.B.2

6.

FLASHCARD QUESTION

Front

What is the Factor Theorem?

Back

Tags

CCSS.HSA.APR.B.2

7.

FLASHCARD QUESTION

Front

Back

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