Question

what is the answer for this question​

Answer 1

Step-by-step explanation:

${2x3}^{3} + {3x}^{2} + ax + b$

$x - 2 = 0$

$x = 2$

$x + 2 = 0$

$x = - 2$

p

$p(x) = {2x}^{3} + {3x}^{2} +ax + b$

p(2)

$p(2) = {2(2)}^{3} + {3(2)}^{2} + a(2) + b$

$p(2) = 2(8) + 3(4) + 2a + b$

$p(2) = 16 + 12 + 2a + b$

$p(2) = 28 + 2a + b$

$p( - 2) = {2( - 2)}^{3} + {3( - 2)}^{2} + a( - 2) + b$

$p( - 2) = 2( - 8) + 3(4) + - 2a + b$

$p( - 2) = - 16 + 12 - 2a + b$

$p( - 2) = - 4 - 2a + b$

from 1 and 2

p(2)=p(-2)

28+2a+b=-4-2a+b

28+4+2a=-2a+b-b

32+2a+2a=0

32+4a=0

4a=-32

a=-32/4

a=-8

from 2

-4-2a+b=0

-4-2(-8) +b=0

-4+16+b=0

12+b=0

b=_12

since a=-8 and b=_12