Quiz about Factoring Polynomials and the Zero Product Property

Question 1

What is the first step in solving
(x + 2)(x - 3) = 0 ?

Accepted Answer

Set each binomial factor equal to zero

Answer

Plug in zero for x

Answer

Solve for x

Answer

FOIL

Question 2

Solve for x

$$5x=0$$

Accepted Answer

x=0

Answer

x=5

Answer

x=2

Answer

x= -5

Question 3

Solve for x

x+5=0

Accepted Answer

x= -5

Answer

x=0

Answer

x=5

Answer

x=2

Question 4

Solve for x

$$x-5=0$$

Accepted Answer

x=5

Answer

x=0

Answer

x=2

Answer

x= -5

Question 5

Solve for x

$$3x-6=0$$

Accepted Answer

x=2

Answer

x=0

Answer

x=5

Answer

x= -5

Question 6

Solve for x

$$\left(x\right)\left(4\right)=0$$

Accepted Answer

x=0

Answer

x=4

Answer

x= -4

Answer

x= 1/4

Question 7

When you multiply, if the answer is 0, then one of the factors must be zero

$$\ if\ ab=0\ $$

then either

$$a=0\ \ \ OR\ \ \ b=0$$

$$0\cdot b=0\ \ \ \ \ \ \ \ \ \ \ \ \ a\cdot0=0$$

Accepted Answer

TRUE

Answer

FALSE

Question 8

$$\left(x+5\right)\left(x-2\right)=0$$

Solve for x:

$$\left(x-5\right)=0\ \ \ \ \ OR\ \ \ \ \ \left(x+2\right)=0$$

Accepted Answer

x=5x= -2

Answer

x=5x=2

Answer

x= -5x= -2

Answer

x= -5x=2

Question 9

Solve for x

$$\left(x+4\right)\left(x+1\right)=0$$

Accepted Answer

x= -4x= -1

Answer

x=4x=1

Answer

x= 4x= -1

Answer

x= -4x=1

Question 10

Solve for x

x(x-4)=0

Accepted Answer

x=0x=4

Answer

x=0x= -4

Answer

x=1x=4

Answer

x= -1x= -4

Question 11

Solve and find your zeros:
z(z - 15)=0

Accepted Answer

z=0 and z=15

Answer

z=0 and z=-15

Answer

z=-15

Answer

z=15

Question 12

What does the zero product property imply about the factors of a product?

Accepted Answer

At least one of the factors must be zero.

Answer

The product of the factors is always one.

Answer

Both factors must be non-zero.

Answer

The factors must be equal.

Question 13

How can you solve an equation using the zero product property?

Accepted Answer

By setting each factor equal to zero and solving for the variable.

Answer

By dividing both sides of the equation by zero.

Answer

By multiplying both sides of the equation by zero.

Answer

By adding the same number to both sides of the equation.

Question 14

What is the first step in solving a polynomial equation using the zero product property?

Accepted Answer

Factor the polynomial.

Answer

Graph the equation.

Answer

Subtract the highest degree term from both sides.

Answer

Set the equation equal to one.

Question 15

If an equation is set to zero and factored into (x - 4)(x + 3) = 0, what are the solutions for x?

Accepted Answer

x = 4 and x = -3

Answer

x = -4 and x = -3

Answer

x = 4 and x = 3

Answer

x = -4 and x = 3

Question 16

Why is it necessary to factor a polynomial before applying the zero product property?

Accepted Answer

To identify the individual factors that could be set to zero.

Answer

To simplify the equation for graphing.

Answer

To convert the polynomial into an exponential equation.

Answer

To increase the degree of the polynomial.

Factoring Polynomials and the Zero Product Property

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