Question

please answer this asap
The best explanation will be marked as brainliest
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Answer 1

if x+2 is the factor of polynomial

ax^3+bx^2+x-2

then,

x+2 = 0

x= -2

p(x) = ax^3 + bx^2+x-2 = 0

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

then

if ax^3+bx^2+x-2 is divided by x-2 and the remainder is 4 then,

then we have to subtract 4 from the polynomial to make the divisor factor

ax^3+ bx^2+x-2 -4 =0

x-2= 0

x= 2

then,

p(x) = ax^3+bx^2+x-6=0

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

then,

We have derived the first equation that -8a +4b -4 = 0

= -8a +4b = 4 ••••(i)

the second equation derived is that

8a +4b -4 = 0

= 8a +4b = 4 ••••(ii)

then equate this

-8a +4b= 8a+4b

-8a = 8a

-16a = 0

a = 0

then,

b can be derived from any equation

8a+4b = 4

4b = 4

b = 1