Chapter 3B review opener

Write a polynomial with x=2 (single root), x= -1 (double root), and x= -3 (double root) and a=4

• $f\left(x\right)=4\left(x-2\right)\left(x+1\right)^2\left(x+3\right)^2$

• $f\left(x\right)=\left(x-2\right)\left(x+1\right)^2\left(x+3\right)^2$

• $f\left(x\right)=4\left(x+2\right)\left(x-1\right)^2\left(x-3\right)^2$

• $f\left(x\right)=4\left(x+2\right)^2\left(x-1\right)^2\left(x-3\right)$

What is the multiplicity of the root at x=1 given the polynomial:  $f\left(x\right)=2\left(x-1\right)^3\left(x+1\right)^2\left(x+3\right)$  

• triple root

• double root

• single root

• quadruple root

Does the polynomial  $f\left(x\right)=-2x^5-5x^2+6$  have a real zero between -1 and 0 ?

• Yes by the IVT

• No by the IVT

What does IVT stand for?

• Isosceles Value Theorem

• Interval Value Theorem

• Intermediate Value Theroem

In order for a polynomial to have a x-intercept (real zero) between two x-coordinates, the y-values must have....

• the same sign

• opposite signs

• absolute value

• squared