Factoring Quadratic Expressions

This video introduces factoring quadratic expressions, focusing on cases where the leading coefficient is one. It explains the anatomy of a quadratic expression and provides examples of factoring when the constant term is positive, negative, or when the middle term is negative. The video emphasizes the importance of identifying correct factor pairs and using signs appropriately.

What is the leading term in a quadratic expression?

• The term with the highest power of x

• The constant term

• The term with the lowest power of x

• The term with no x

In the expression x^2 + 7x + 12, which pair of numbers should be used to factor it?

• 5 and 7

• 3 and 4

• 2 and 6

• 1 and 12

When factoring x^2 + 7x + 12, why do we choose the pair 3 and 4?

• Because they are consecutive numbers

• Because they are both prime numbers

• Because they multiply to 7 and add to 12

• Because they multiply to 12 and add to 7

For the expression x^2 + 7x - 18, which pair of numbers should be used to factor it?

• 6 and -3

• 3 and -6

• 9 and -2

• 1 and -18

Why is it important to consider both positive and negative factors when the constant term is negative?

• To ensure the middle term is positive

• To find a pair that adds to the middle term

• To avoid complex numbers

• To make the expression simpler

In the expression x^2 - 7x + 10, why do we consider negative factors?

• Because the constant term is negative

• Because the middle term is negative

• Because both terms are negative

• Because the expression is not factorable

Which pair of numbers is used to factor x^2 - 7x + 10?

• 1 and 10

• -1 and -10

• -2 and -5

• 2 and 5

What should you always check when there is a negative sign in the quadratic expression?

• The positive factors of the constant term

• The negative factors of the constant term

• The prime factors of the constant term

• The even factors of the constant term

What is the role of the constant term in factoring quadratic expressions?

• It affects the choice of factors

• It determines the leading coefficient

• It is always negative

• It is always positive

What is a key tip for factoring quadratic expressions with negative signs?

• Ignore the negative signs

• Only consider positive factors

• Always check negative factors

• Use a calculator