Setting Factors Equal to Zero

Convert x²+6x+9 to factored form and identify the solution.

• (x+3)(x+3); x=-3

• (x+4)(x+5); x=-4, -5

• (x-3)(x-3); x=3

• Not factorable

If a quadratic equation can be factored into (x - 3)(x + 2) = 0, what are the solutions for x?

• x = 0, x = 1

• x = 4, x = -3

• x = 5, x = -1

• x = 3, x = -2

If a quadratic equation can be factored into (x + 5)(x - 4) = 0, what are the solutions for x?

• x = -5, x = 4

• x = -3, x = 2

• x = 0, x = 9

• x = 1, x = 6

What are the key steps to apply the zero product property to solve a quadratic equation?

• Set each factor equal to zero and solve for the variable.

• Set each factor equal to one and solve for the variable.

• Add the factors together and solve for the variable.

• Multiply the factors and solve for the variable.

What is the zero product property?

• If the product of two real numbers is zero, then at least one of the numbers must be zero.

• If the product of two real numbers is zero, then both numbers must be zero.

• If the difference of two real numbers is zero, then both numbers must be zero.

• If the sum of two real numbers is zero, then both numbers must be zero.

How is the zero product property related to quadratic equations?

• The zero product property has no relation to quadratic equations

• Quadratic equations are solved by adding the zero product to the equation

• Quadratic equations can be solved using the zero product property by setting the equation equal to zero and factoring it to find the solutions.

• Quadratic equations cannot be solved using the zero product property

Explain how the zero product property can be used to solve real-world problems involving quadratic equations.

• By using the quadratic formula to find the solutions

• By setting the equation equal to zero and factoring it to find the values of the variable that satisfy the equation.

• By dividing the equation by zero

• By adding the coefficients of the quadratic equation

How are factors related to x-intercepts?

• They are the same

• They are not related

• x-intercepts are found by setting the factors=0

• x-intercepts are found by setting x=0

Which of the following is a completely factored polynomial?

• f(x)=2x⁴-3x³+8x-6

• f(x)=x²(x-1)(x+3)

• f(x)=x(x²-16)

• f(x)=(2x+1)(x²-3x-18)

If (x + 3) divides a polynomial function evenly, then which of these is known to be a zero of the polynomial?

• x = -3

• x = 3

• x = 0

• cannot be determined