Polynomial Zeros and Their Properties

The video tutorial explains how to find the zeros of a polynomial by first simplifying it, combining like terms, and applying the diamond method for factoring. The process involves solving for zeros and verifying the solutions using a graphing tool. The tutorial highlights the importance of understanding polynomial structures and methods for solving them.

What is the first step in simplifying the polynomial to find its zeros?

• Factor out the common variable

• Add a constant to all terms

• Divide all terms by the highest power

• Multiply all terms by a constant

After factoring out the common term, what is the next step in simplifying the polynomial?

• Use synthetic division

• Apply the quadratic formula

• Graph the polynomial

• Combine like terms

What method is used to factor the polynomial after combining like terms?

• Completing the square

• Quadratic formula

• Synthetic division

• Diamond method

Which of the following is a correct pair of numbers that multiply to -18 and add to 7?

• 9 and -2

• 6 and -3

• 3 and -6

• 2 and -9

What is the nature of the solution for the equation X^2 + 9 = 0?

• Two real solutions

• One real solution

• Infinite solutions

• No real solution

What is the approximate value of the square root of 2?

• 1.73

• 1.41

• 1.00

• 2.00

What is the result of solving the equation X^2 - 2 = 0?

• X = ±3

• X = ±√2

• X = ±2

• X = ±1

What is the significance of a 'no real solution' in the context of polynomial zeros?

• The polynomial has complex x-intercepts

• The polynomial has a single x-intercept

• The polynomial has infinite x-intercepts

• The polynomial has no x-intercepts

How many times does the polynomial cross the x-axis according to the graph?

• Four times

• Twice

• Once

• Three times

Which tool is used to verify the number of times the polynomial crosses the x-axis?

• Mathematica

• Excel

• Desmos

• Calculator