Question

verify x=2 is the zero polynomial p(x) =4xcube -3xsquare-6x+32​

Answer 1

Answer:

x = 2 is not a zero of polynomial p(x) = 4x³ - 3x² - 6x + 32.

Step-by-step explanation:

If substituting x = 2 in polynomial p(x) = 4x³ - 3x² - 6x + 32 gives final result = 0.

Then, x = 2 will be zero of the given polynomial p(x) = 4x³ - 3x² - 6x + 32.

p(x) = 4x³ - 3x² - 6x + 32    ——————— (i)

substituting x = 2 in (i)

p(2) = 4 × (2)³ - 3 × (2)² - 6 × (2) + 32

       = 4 × 8 - 3 × 4 - 6 × 2 + 32

       = 32 - 12 - 12 +32

       = 40 ≠ 0

∵ Final result of p(2) ≠ 0

∴ x = 2 is not a zero of polynomial p(x) = 4x³ - 3x² - 6x + 32.

Answer 2

$verify \: x=2 \: is \: the \: zero \: polynomial \: \\ p(x) = {4x}^{3} - {3x}^{2} -6x+32 \\ solution \\ p(x) = {4x}^{3} - {3x}^{2} -6x+32 \\ p(2) = 4( {2)}^{3} - 3( {2)}^{2} - 6(2) + 32 \\ = 32 - 12 - 12 + 32 \\ = 64 - 24 \\ = 40 \: \: \: remainder.$