Remainder and Factor Theorems, Sum and Diff of Cubes

Is (x-4) a factor of (x³ +x² -16x-16)?

• YES
• NO

Tags

CCSS.HSA.APR.B.2

Is (x-3) a factor of
(x³ - 3x² + 2x + 2)?

• Yes
• No

Tags

CCSS.HSA.APR.B.2

What is the proper way to write the answer for the following problem? Each term of the original polynomial is represented in the table.

• 2x³-x²-25x-12

• 2x⁴-x³-25x²-12x+0

Find all the factors of   x³ -3x² -4x +12 given that -2 is a zero.

• (x-2) (x+2) (x+3) 
• (x-2) (x-2) (x+3)
• (x+2) (x+2) (x+3)
• (x-2) (x+2) (x-3)

Tags

CCSS.HSA.APR.B.2

Find all the real zeros of the function 
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

• x = 1/2, -6
• x = -1/2, 6
• x = 4, -1/2, 6
• x = -4, 1/2, -6

Tags

CCSS.HSA.APR.B.2

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3
• -1,-3,3/2
• 3,3,3
• -3,2/3,-1

Tags

CCSS.HSF-IF.C.7C

Factor:  27x³ + 8

• (3x + 2)(9x² - 6x + 4)
• (9x + 2)(3x² + 18x + 4)
• (3x²+4)(9x + 2)
• (27x + 8)(x² - 216x + 64)

Tags

CCSS.HSA.APR.C.4

Solve

8x³+125=0

• x=-5/2, x=(-5±5i√3)/4

• x=-5/2, x=(5±5i√3)/4

• x=-2/5, x=(-5±5i√3)/4

• x=-2/5, x=(5±5i√3)/4

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

Tags

CCSS.HSF-IF.C.7C

The degree of the polynomial determines the number of roots.

• True
• False

Tags

CCSS.HSN.CN.C.9