How do you factor a trinomial of the form $$x^2 + bx + c$$ ?

To factor a trinomial of the form $$x^2 + bx + c$$ , find two numbers that multiply to $$c$$ and add to $$b$$ . Then, write it as $$(x + m)(x + n)$$ where $$m$$ and $$n$$ are the two numbers.

What is the general form of a quadratic equation?

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ where $$a$$ , $$b$$ , and $$c$$ are constants.

What is the leading coefficient in a polynomial?

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

How do you identify a perfect square trinomial?

A perfect square trinomial can be identified if it can be expressed as $$(a + b)^2 = a^2 + 2ab + b^2$$ or $$(a - b)^2 = a^2 - 2ab + b^2$$ .

What is the first step in factoring a polynomial?

The first step in factoring a polynomial is to look for a common factor in all terms.

Factor the expression: $$16x^2 + 25$$

Prime (it cannot be factored further).

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

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.

Factoring Difference of Squares and Trinomials a = 1 Flashcards

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1.

FLASHCARD QUESTION

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What is the difference of squares formula?

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials.

5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

Front

What is the sum of cubes formula?

Back

7.

FLASHCARD QUESTION

Front

What is the product of a sum and difference?

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