Solving Equations by Factoring Quiz

What is the key principle when the product of factors equals zero?

• All factors must be zero.

• At least one factor must be zero.

• None of the factors can be zero.

• The product must be greater than zero.

In the equation 2x - 3 * x + 5 = 0, what are the possible values of x?

• x = 3/2 and x = 5

• x = 3/2 and x = -5

• x = -3/2 and x = 5

• x = 3 and x = -5

How do you start solving a non-factored polynomial equation?

• Multiply all terms by the leading coefficient.

• Add the terms on both sides.

• Set all terms to one side and zero on the other.

• Divide all terms by the highest coefficient.

In the equation x^2 + 7x + 6 = 0, what are the factors of 6 that add up to 7?

• 2 and 3

• 1 and 6

• 3 and 4

• 5 and 1

What is the first step in factoring a polynomial with a greatest common factor?

• Subtract the GCF from both sides.

• Add the GCF to both sides.

• Multiply the polynomial by the GCF.

• Factor out the GCF from the polynomial.

What is the result of factoring x^2 - 3x - 10?

• (x + 5)(x + 2)

• (x - 5)(x + 2)

• (x + 5)(x - 2)

• (x - 3)(x + 3)

Why should you avoid dividing by the variable you are solving for?

• It can lead to incorrect solutions.

• It simplifies the equation too much.

• It makes the equation more complex.

• It is mathematically incorrect.

What should you do if a polynomial does not factor?

• Use alternative methods to solve it.

• Ignore the polynomial.

• Divide by the highest coefficient.

• Add terms to both sides.

What is the solution to the equation x(x - 5) = 0?

• x = 5 or x = 10

• x = 0 or x = -5

• x = 5 or x = -5

• x = 0 or x = 5

What is the general rule of thumb regarding the greatest common factor?

• Always divide by the GCF.

• Multiply by the GCF.

• Never divide by a variable GCF.

• Ignore the GCF.