Factoring Quadratics: The Sum-Product Method

What is the primary goal when factoring second degree expressions?

• To determine the coefficient of the x term

• To simplify the expression to its lowest terms

• To find the roots of the quadratic equation

• To rewrite the expression in a product of binomials

What do the letters 'a' and 'b' represent in the process of multiplying out (x + a)(x + b)?

• The roots of the quadratic equation

• The sum and product needed for factoring

• The constants in the binomials

• The coefficients of the x terms

How do you determine the correct numbers for 'a' and 'b' when factoring?

• By selecting numbers that add up to the constant term

• By guessing until the correct numbers are found

• By finding numbers whose sum equals the coefficient of x and whose product equals the constant term

• By choosing any two numbers that multiply to the constant term

In the first example, what are the values of 'a' and 'b' that satisfy the conditions for factoring?

• a = 4, b = 10

• a = -4, b = -10

• a = 10, b = 4

• a = -10, b = -4

What does a positive constant term in the quadratic expression indicate about the signs of 'a' and 'b'?

• The signs of 'a' and 'b' are irrelevant

• Both 'a' and 'b' are negative

• Both 'a' and 'b' are positive

• One is positive and the other is negative

What is the factored form of the expression in the first example?

• x - 10 * x - 4

• x + 4 * x + 10

• x + 10 * x + 4

• x - 4 * x - 10

In the second example, what is the coefficient of the x term?

• 1

• 12

• -12

• -1

What does a negative product of 'a' and 'b' indicate about their signs?

• Both are negative

• Both are positive

• They have different signs

• Cannot be determined

Which pair of numbers satisfies both conditions for factoring in the second example?

• 3 and -4

• 3 and 4

• -3 and 4

• -3 and -4

How is the factored expression written in the second example?

• x - 4 * x + 3

• x + 4 * x - 3

• x - 3 * x + 4

• x + 3 * x - 4