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

To factor $$x^2 + bx + c$$ , find two numbers that multiply to c and add to b, then express the quadratic as $$(x + m)(x + n)$$ where m and n are the two numbers.

What is a perfect square trinomial?

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as $$(x + a)^2 = x^2 + 2ax + a^2$$ .

What is the difference of squares?

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

How do you check if your factoring is correct?

To check if your factoring is correct, multiply the factors back together and see if you obtain the original expression.

What is the significance of the leading coefficient in factoring quadratics?

The leading coefficient (a) affects the shape and direction of the parabola represented by the quadratic equation, and it must be considered when factoring.

What is the first step in factoring a quadratic expression?

The first step in factoring a quadratic expression is to look for a common factor in all terms, if one exists.

Factoring Quadratics Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

2.

FLASHCARD QUESTION

Front

What is a quadratic expression?

Back

3.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

5.

FLASHCARD QUESTION

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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