How do you factor the expression $$4h^2 - 12h + 9$$ ?

The expression factors to $$ (2h - 3)^2 $$ .

What are the roots of the quadratic equation $$x^2 + 9x - 36 = 0$$ ?

The roots are $$x = -12$$ and $$x = 3$$ .

What is the process to factor a quadratic expression?

1. Identify a, b, and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping.

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

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

How do you factor the expression $$x^2 + 9x - 36$$ ?

The expression factors to $$ (x + 12)(x - 3) $$ .

A binomial is a polynomial with two terms, such as $$a + b$$ or $$x^2 - 4$$ .

What is the relationship between the factors and roots of a quadratic?

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the factors of the quadratic.

How do you determine if a quadratic expression is prime?

A quadratic expression is prime if it cannot be factored into the product of two binomials with real coefficients.

What is the factored form of $$20x^2 + 13x + 2$$ ?

The expression factors to $$ (4x + 1)(5x + 2) $$ .

How do you factor the expression $$2x^2 - 11x + 12$$ ?

The expression factors to $$ (2x - 3)(x - 4) $$ .

What is the importance of factoring quadratics in solving equations?

Factoring quadratics allows us to rewrite the equation in a simpler form, making it easier to find the roots or solutions.

Factoring Quadratics (HA2) Flashcards

Student preview

16 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, 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 does it mean for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as a product of two binomials.

5.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

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