Applying Descartes rule of signs with all positive terms

The video tutorial explains how to use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros of a polynomial function. The instructor demonstrates the process by evaluating the polynomial for changes in sign, first for positive zeros and then for negative zeros by substituting negative values. The conclusion highlights the importance of understanding sign changes to predict the number of real zeros accurately.

What does Descartes' Rule of Signs help determine in a polynomial function?

• The number of positive and negative real zeros

• The degree of the polynomial

• The roots of the polynomial

• The coefficients of the polynomial

When evaluating a polynomial for negative real zeros, what is the first step?

• Substitute negative x into the polynomial

• Factor the polynomial

• Graph the polynomial

• Differentiate the polynomial

How does a negative number raised to an even power behave?

• It becomes undefined

• It becomes positive

• It becomes zero

• It remains negative

What is the significance of sign changes in Descartes' Rule of Signs?

• They indicate the degree of the polynomial

• They show the number of terms in the polynomial

• They reveal the polynomial's symmetry

• They determine the possible number of real zeros

What should you conclude if the number of real zeros does not match Descartes' Rule of Signs?

• The polynomial has complex roots

• The rule was applied incorrectly

• The polynomial is linear

• The polynomial is incorrect