How to find the zeros of a polynomial using the sum of two cubes

The video tutorial covers the process of factoring expressions, starting with identifying the greatest common factor (GCF) and using the sum of cubes formula. It then moves on to simplifying the factored form and solving equations using the zero product property. The tutorial also explains how to handle non-factorable equations using the quadratic formula and discusses complex solutions, emphasizing the difference between real and complex solutions in terms of x-intercepts.

What is the first step in factoring a polynomial that is a sum or difference of cubes?

• Factor out the greatest common factor

• Apply the quadratic formula

• Set the equation to zero

• Identify the cube roots

When factoring a sum of cubes, what is the formula used to express the polynomial in its factored form?

• a^3 + b^3 = (a - b)(a^2 + ab + b^2)

• a^3 - b^3 = (a + b)(a^2 - ab + b^2)

• a^3 + b^3 = (a + b)(a^2 - ab + b^2)

• a^3 - b^3 = (a - b)(a^2 + ab + b^2)

What property is used to solve a polynomial equation once it is factored?

• Commutative Property

• Associative Property

• Zero Product Property

• Distributive Property

Which method can be used to solve a non-factorable quadratic equation?

• Long division

• Synthetic division

• Graphing

• Completing the square

How many solutions does a cubic polynomial have based on its degree?

• Four

• Three

• Two

• One

Why can't complex solutions be graphed on the real number axis?

• They are too large

• They require a logarithmic scale

• They are undefined

• They need an imaginary axis

What is the relationship between real solutions and x-intercepts of a polynomial?

• Complex solutions are x-intercepts

• Only real solutions are x-intercepts

• All solutions are x-intercepts

• There is no relationship