Finding Zeros and Multiplicity

What do "zeros" represent?

• something a polynomial can not be.

• the place that the polynomial crosses the x axis/ the x value that makes the whole equation equal to zero

• the place that the polynomial crosses the y axis/ the y value where x=0

• the number zero

Tags

CCSS.HSF-IF.C.7C

To find zeroes of polynomials, we...

• say x=0

• make pancakes

• ask NASA

• set factors equal to zero

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

• 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

• 2 (Mult of 3), 7 (mult 1)

• 0, 2, 7

• 2 (mult of 2), 7 (mult of 3)

Tags

CCSS.HSF-IF.C.7C

• 2

• 4

• 6

• 1

Tags

CCSS.HSF-IF.C.7C

Tags

CCSS.HSF-IF.C.7C

• 2

• 1

• 4

• 3

Tags

CCSS.HSF-IF.C.7C

State the zeros of the polynomial (include multiplicity):
f(x) = x(x+3)²(x - 2)

• x = 0, 3, 2

• x = 0, -3 (multiplicity of 2), 2

• -3, 2

• 0, 2 (multiplicity of 3)

Tags

CCSS.HSF-IF.C.7C

State the zeros of the polynomial (include multiplicity):

• zeros = 0, 3, 2 (all multiplicity 1)

• zeros = 0, -3 (multiplicity of 2), 2

• zeros = -3 (multiplicity 2), and 2

• zeros = 0, 2 (multiplicity of 3)

Tags

CCSS.HSF-IF.C.7C

What is the multiplicity of the zero x=-5 for the function f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)?

• 1

• 2

• 3

• 4

Tags

CCSS.HSF-IF.C.7C

If the there is a turning point (bounce) on the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

Tags

CCSS.HSF-IF.C.7C