Polynomial Review

Factoring is FUN

100

Factor Completely.

6n³ - 2n² + 21n - 7

(2n²+7)(3n-1)

200

Factor Completely.

3n³ - 18n² + 15n

3n(n-5)(n-1)

300

Factor Completely.

16x⁴ - 1

(4x² + 1)(2x+1)(2x-1)

400

Factor Completely.

64u³ + 1

(4u + 1)(16u² - 4u +1)

500

Factor Completely.

27x³ - 8y³

(3x - 2y)(9x² + 6xy + 4y²)

ROOTS

100

Find the possible # of real roots for the polynomial  

  x³ + x² + 4x + 4 = 0.

Possible # of real roots: 3 or 1

200

Find the rational root (s) of the polynomial 

x³ + x² + 4x + 4 = 0.

Rational Root: {-1}

300

Find the possible rational roots of the polynomial function: 

f(x)= 4x³ + 8x² + 5x + 1

+/- (1, 1/2, 1/4)

400

Find the zeros of the function 

f(x)= 4x³ + 8x² + 5x + 1.

{-1/2 mult. of 2, -1}

500

Find all roots of the function

 f(x)=x³ + 3x² + 4x + 2 . 

x = -1 , -1 + i, -1 - i

anything POLYNOMIAL

300

Find a polynomial of least degree (in standard form) that has integer coefficients given the zeros: 

{-2, 3, -4}

f(x)= x³ + 3x² - 10x - 24

400

Factor Completely.

x⁶ - 2x³ + 1

(x - 1)²(x² + x + 1)²

500

Write a polynomial function (in factored form) of least degree with integer coefficients, no square roots or iʻs,  and has the given zeros.

-2, 1/3, 1 + √3 i 

f(x) = (x+2)(3x-1)(x² - 2x + 4)