Factor of Polynomial Function

Polynomial equation x⁴ - 4x³ + 5x² - 4x + 4 = 0 has a solution of x = 2.  Is this synthetic division set up correctly in order to find factors of the polynomial?

• yes

• no

Polynomial function f(x) =  x⁴ - 4x³ + 5x² - 4x + 4 is known to have a zero of x = 2 with a multiplicity of 2. Does this mean (x - 2) divides the polynomial twice?

• yes

• no

(x - 2) divides polynomial function
 f(x) =  x⁴ - 4x³ + 5x² - 4x + 4 two times.  Which of these is a complete factorization of f(x)?

• (x - 2)²(x - 1)(x + 1)

• (x - 2)² (x + 1)

• (x - 2)²(x² + 1)

• cannot be determined

Factor this expression:
2x³ + 2x² - 24x

• 2x(x + 4)(x - 3)

• 2x(x - 4)(x - 3)

• 2x(x - 4)(x + 3)

• none of these

Factor x^3 - 2x^2 + x

• x(x - 1)(x + 1)

• x(x - 1)^2

• (x^2 - 1)(x + 1)

• (x^2 - 1)(x - 1)

Factor 3x^5 - 3x^3

• (3x^2 - 1)(x^3 + 1)

• 3x^3(x - 1)(x + 1)

• (3x^3 + 2)(x^2 - 6)

• x^3(3x^2 - 1)

Factor x^4 - x^2 - 30

• (x^2 + 6)(x^2 - 5)

• (x^3 + 6)(x - 5)

• (x^2 - 6)(x^2 + 5)

• (x + 6)(x^3 - 5)

Factor x^4 - 4x^2 - 21

• (x^2 - 7)(x^2 + 3)

• (x^2 + 7)(x^2 - 3)

• (x^2 + 1)(x^2 - 21)

• (x^2 - 1)(x^2 + 21)

Factor f(x)= x³ - 2x²-13x - 10  given that
(x - 5) is one factor.

• (x- 5)(x - 1)(x - 2)

• (x - 5)(x + 2)(x - 2)

• (x - 5)(x + 2) (x + 1)

• (x - 5)(2x - 13)

Consider a polynomial function p(x), a is a real number and if x = a is a zero of p, then (x - a) is a linear factor of p.

• TRUE

• FALSE