2.2 sections work on zero

Question

Find the real zeros of f and state multiplicity for each zero with the graph of f touching the x-axis at each zero

1.) f(x) = 3(x-1)(x+2))(x-3)

2.) f(x) = (x+2)²(2x+1)

3.f(x) = -x²(x²-9)(3x+2)³

Answer 1

The question has some poorly worded instructions.

"and state multiplicity for each zero with the graph of f touching the x-axis at each zero"

I believe your teacher wanted you to state the multiplicities of all zeros. But I think your teacher also wanted you to indicate that the graph touches (is tangent to but does not cross) the x-axis when the multiplicity is even.

Polynomials only cross the x-axis when the multiplicities are odd numbers.

Answer 2

Set each factor equal to zero. The exponent on the outside of each factor is your multiplicity.

1) zeros: x= 1, -2, 3 all with multiplicity 1

2) zeros: x= -2 (multiplicity 2), -1/2 (multiplicity 1)

3) zeros: x= 0 (multiplicity 2), ±3 (each multiplicity 1), -2/3 (multiplicity of 3)

Hope this helps!