What is the zero-product property?

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if $$(x - 3)(x + 2) = 0$$ , then $$x - 3 = 0$$ or $$x + 2 = 0$$ .

How do you factor a quadratic polynomial?

To factor a quadratic polynomial, look for two numbers that multiply to $$ac$$ (the product of the leading coefficient and the constant term) and add to $$b$$ (the coefficient of the linear term).

What is the difference of squares?

The difference of squares is a special factoring pattern that states $$a^2 - b^2 = (a - b)(a + b)$$ .

What is a perfect square trinomial?

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, such as $$a^2 + 2ab + b^2 = (a + b)^2$$ .

What is the role of the leading coefficient in factoring?

The leading coefficient is the coefficient of the highest degree term in a polynomial. It affects the shape and direction of the graph of the polynomial.

What is synthetic division?

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form $$(x - c)$$ .

How can you check if your factorization is correct?

You can check if your factorization is correct by multiplying the factors back together to see if you obtain the original polynomial.

What is the significance of factoring in solving polynomial equations?

Factoring is significant in solving polynomial equations because it allows us to find the roots or solutions of the equation by setting each factor equal to zero.

Factoring Polynomials Completely 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 factor a polynomial?

Back

3.

FLASHCARD QUESTION

Front

What is the greatest common factor (GCF)?

Back

4.

FLASHCARD QUESTION

Front

How do you find the GCF of polynomial terms?

Back

To find the GCF of polynomial terms, identify the common factors in the coefficients and the lowest power of each variable present in the terms.

5.

FLASHCARD QUESTION

Front

What is the first step in factoring a polynomial completely?

Back

The first step in factoring a polynomial completely is to factor out the greatest common factor (GCF) from all the terms.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is a quadratic polynomial?

Back

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