Factoring Polynomial Functions

What is the multiplicity of a zero/root?

• The highest exponent of a polynomial

• The number of different factors

• The exponent of the factor corresponding to that root

• The number in front of a polynomial

Select the polynomial whose zeros and degree are as follows:

-5 (Mult of 3), 9 (Mult of 2), – 2, 4 with Degree: 7

• (x + 5)³(x - 9)²(x + 2)(x - 4)

• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

• (x + 5)³(x - 9)²(x + 2)

• (x + 5)(x - 9)(x + 2)(x - 4)

Multiplicity

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

How can I tell, when doing polynomial division, if the binomial is a FACTOR of the dividend?

• The remainder is zero

• They are all factors

• We can't tell

• The remainder is a constant

• 2

• 1

• 4

• 3

Which root has even multiplicity?

• 1

• -4

• -1

• 2

Factor  by grouping:
20x² - 16x - 25x +20

• (20x - 5)(x - 4)

• (4x + 5)(5x + 4)

• (5x - 4)(4x - 5)

• (5x + 4)(4x - 5)

Factor the trinomial:
x² - 4x - 12 

• (x - 6)(x - 2)

• (x - 8)(x + 2)

• (x - 6)(x + 2)

• (x + 6)(x - 2)

Factor the trinomial:
x² - 6x + 9 

• (x + 3)²

• (x + 3)(x - 3)

• (x - 9)(x - 3)

• (x - 3)²

Factor the binomial:
9x² - 25

• (3x - 5)(3x + 5)

• (3x - 5)(3x - 5)

• (3x + 5)(3x + 5)

• (9x + 5)(x - 5)